MATH U1

Find the discriminant of x2−10x+3=0.

88

What value of k will make the following expression a perfect square trinomial? s2−3s+k −32 32 9/4 −94

9/4

Given the quadratic equation 3x + 6x^2 = -5, what are the values of a, b, and c? a = 3, b = 6, c = -5 a = 6, b = 3, c = 5 a = 3, b = 6, c = 5 a = 6, b = 3, c = -5

a = 6, b = 3, c = 5

Which of the following is the quadratic formula? Incorrect x=−b±√b2+4ac2ax=−b±b2+4ac2a x=−b±√b2−4ac2ax=−b±b2−4ac2a x=b±√b2+4ac2ax=b±b2+4ac2a x=b±√b2−4ac2ax=b±b2−4ac2a

x = -b + √ b^2 - 4ac / 2a

Solve the quadratic equation x2−x=1. x=−1±√52x=−1±52 x=1±√32x=1±32 x=−1±√32x=−1±32 x=1±√52x=1±52

x = 1 ± √5 / 2

Solve the quadratic equation 2x2+7x−4=0. x=−14;x=2x=−14;x=2 x=12;x=−4x=12;x=−4 x=14;x=−2x=14;x=−2 x=−12;x=4x=−12;x=4

x = 1/2; x = −4

Solve the quadratic equation (x−2)2−18=0 x=−2±2√3x=−2±23 x=−2±3√2x=−2±32 x=2±3√2x=2±32 x=2±2√3x=2±23

x = 2 ± 3√2

Solve the quadratic equation 6x2+8x=8 x=−23x=−23 and x=2 x=23x=23 and x=2x=2 x=−23x=−23 and x=−2x=−2 x=23x=23 and x=−2x=−2

x = 2/3 and x = −2

Solve the quadratic equation x2−2x=3 x=−3,−1x=−3,−1 x=−3,1x=−3,1 x=3,−1x=3,−1 x=3,1x=3,1

x = 3, −1

Solve the quadratic equation 2x(x+5)=0. x=0,−5 x=−2,−5 x=0,5 x=2,−5

x=0,−5

How many solutions does the equation a4−5a2+6=0 have? Incorrect 2 5 4 3

4

What is the discriminant of x2=0x2=0?

0

Solve for the discriminant of 4x2−x+8=0.

-127

What is the product of the solutions of 3+6y−2y2=0? Correct 33 −32−32 −3−3 3232

-3/2

What should be the value of k so that the equation 6x2+kx−10=0 is the same as (3x−2)(2x+5)=0? −10 10 −11 11

11

What should be the value of k so that the equation 10x2−kx−6=0 is the same as (2x−3)(5x+2)=x? Correct -11 -12 12 11

12

Which of the following is the square root of −16? i√4 4 4i −4

4i

The difference of a positive number and its square is −30. Find the number. 5 -5 -6 6

6

Identify the nature of the roots of 9x^2−6x−5=0. Correct three real roots no real root / imaginary roots one real root / two equal roots two distinct real roots

two distinct real roots

Identify the nature of the roots of the equation x^2+√5x−√3. Correct no real root / imaginary roots three real roots two distinct real roots one real root / two equal roots

two distinct real roots

Supply the correct quantities to complete the equation below. 4s2−4s−3=0 (□s−□)(□s+□)=0 Correct 2,1,2,3 1,1,4,3 2,3,2,1 4,1,1,3

2,3,2,1

What is the sum of the solutions of x2−3x−3=0? Correct −32− 32 −3 3

3

Write a quadratic equation with a=3, b=−1, and c=0. 3x2−x−1=03x2−x−1=0 3(y−1)2+5y=33(y−1)2+5y=3 3w2−(w+1)=13w2−(w+1)=1 3z(z−1)=03z(z−1)=0

3(y−1)^2 + 5y = 33

A square lot has an area of 176 square meters. Find the length of one side of the lot. 44 meters ±4√111 meters 4√11 meters 13 meters

4√11 meters

True or False: d = 4ac − b^2

False

Given the quadratic equation −x + 4x(2 − x) = -1 - x + 4x(2 - x) = -1, what are the values of a, b, and c? a = -4, b = -9, c = -1 a = 4, b = -7, c = -1 a = 4, b = -9, c = 1 a = -4, b = 7, c = -1

a = b=−7, c=−1

Use the quadratic formula to solve x2−4x−8=0. Correct x=−2±2√3x=−2±23 x=2±4√3x=2±43 x=−2±4√3x=−2±43 x=2±2√3x=2±23

x = 2 + 2√3

Solve the quadratic equation 2x−x(2−x)=12. x=±3i√5x=±3i5 x=±2√3x=±23 x=±i√6x=±i6 x=±√6x=±6

x = ± 2√3

What are the solutions of the quadratic equation (x−3)(x−4)=0? x=3 and x=−4x x=−3x and x=4 x=−3 and x=−4 x=3 and x=4

x=3 and x=4

By completing the square, the quadratic equation 2y2−3y+2=0 is rewritten as (y−k)2=c. Find the values of k and c k=34k=34 and c=−12c=−12 k=32k=32 and c=−716c=−716 k=32k=32 and c=−12c=−12 k=34k=34 and c=−716c=−716

k = 34 and c = −716

By completing the square, the quadratic equation 3y2−5y+3=0 is rewritten as y2+ky+c=−1+c. Find the values of k and c. k=53k=53 and c=2536c=2536 k=53k=53 and c=259c=259 k=−53k=−53 and c=259c=259 k=−53k=−53 and c=2536c=2536

k = −5/3k and c = 25/36

By completing the square, the quadratic equation 2x2−8x+1=0 is rewritten as x2−kx+c=−12+c. Find the values of k and c. k=−8k=−8 and c=16c=16 k=4k=4 and c=4c=4 k=8k=8 and c=16c=16 k=−4k=−4 and c=4c=4

k=4 and c=4

What is the nature of the roots of 8x=−7x^2−4? Correct no real root / imaginary roots three real roots one real root / two equal roots two distinct real roots

no real root / imaginary roots

Determine the nature of the roots of the equation 4x^2=0. Correct no real root / imaginary roots three real roots two distinct real roots one real root / two equal roots

one real root / two equal roots

In what formula is the discriminant related to?

quadratic formula

Arrange the following steps in solving the equation y4−13y2+36=0. Let u=y2

u2−13u+36=0 (u−9)(u−4)=0 u=9;u=4 y2=9;y2=4 y=±3;y=±2

If the equation a4−5a2+6=0 is transformed into a quadratic equation, which of the following is the result? Let u=a^2. Correct u2−5u+6=0u2−5u+6=0 u2+5u+6=0u2+5u+6=0 u4−5u2+6=0u4−5u2+6=0 u4−5u+6=0u4−5u+6=0

u^2 - 5u + 6 = 0

Which of the following representations can be used so that the equation 4√w+2√w=3 is transformed to quadratic equation? Correct u=w4 u4=w u=w2 u2=w

u^4 = w

Which of the following is the simplest form of √180? 4√11.25 3√20 6√5 2√45

6√5

What are the solutions of the equation 4√w+2√w=3w4+2w=3? Correct 1 16/81 81/16 −1

1 81/16

What value of kk will make the following expression a perfect square trinomial? h2+10h+k 25 15 5 10

25

If u^4=w in the equation 4√w+2√w=3, what is its corresponding quadratic equation? Correct u2−2u−3=0 u2+2u−3=0 2u2−u−3=0 2u2+u−3=0

2u^2+u−3=0

Which of the following is NOT a quadratic equation? 4x^2 = -2x^2 2x^2 − 3√x - 1 = 0 √3x + √5x^2 - 6 = 0 2x^3 + 3x^2 - 2x^3 + 4 = 0

2x^2 − 3√x − 1 = 0

A number is one less than twice another number. The product of the two numbers is thrice the larger number. Let y represent the smaller number. Which of the following equations can be used to find the two numbers? 2y2+7y−3=02y2+7y−3=0 2y2+7y+3=02y2+7y+3=0 2y2−7y−3=02y2−7y−3=0 2y2−7y+3=02y2−7y+3=0

2y^2 − 7y + 3 = 0

Solve the equation (r−2)4−3(r−2)2=10(r−2)4−3(r−2)2=10. Correct 2±√5 −2±i√2 2±i√2 −2±√5

2±√5 2±i√2

Supply the correct quantities to complete the equation below. 6h2+3h=0 (□h+□)(□h+□)=0 3,0,2,1 6,0,1,3 1,3,6,1 2,1,3,1

3,0,2,1

The height h (in feet) of a cannonball launched upward is modeled by the equation h=−16t2+48t+164 where t is the time in seconds. How many seconds will it take the cannonball to reach a height of 100 ft? Correct 8 seconds 4 seconds 16 seconds 1 second

4 seconds

What is the function of the discriminant of a quadratic equation? Incorrect It indicates the roots of a quadratic equation. It indicates the nature of the roots of a quadratic equation. It indicates the values of a, b and c. It indicates the sign of the roots of a quadratic equation.

It indicates the roots of a quadratic equation.

Is 1/x^2 + 2/x = 0 a quadratic equation? No, because there is no constant term on the left side of the equation. Yes, because the highest exponent is 2. Yes, because the equation can be multiplied by x2x2. No, because there are terms with variables in the denominator

No, because there are terms with variables in the denominator.

One of the solutions of a certain quadratic equation is imaginary. Which of the following is true? Correct The coefficients are all negative. The other solution is also imaginary. The value of cc is negative. The quadratic equation is factorable.

The other solution is also imaginary.

Given the quadratic equation (x−2)(2x+4)=12, what are the values of a, b, and c? Correct a=2a=2, b=8b=8, and c=−12c=−12 a=2a=2, b=8b=8, and c=−20c=−20 a=2, b=0, c=−20 a=2a=2, b=0b=0, and c=−12c=−12

a=2, b=0, c=−20

The length of a rectangular cardboard is two inches more than its width. The area of the cardboard is 8in^2. Letting w as the width of the cardboard, which of the following quadratic equations can be used to find the dimensions of the cardboard? Correct w2−2w−8=0w2−2w−8=0 w2+2w+8=0w2+2w+8=0 w2+2w−8=0w2+2w−8=0 w2−2w+8=0w2−2w+8=0

w^2 + 2w − 8 = 0

Solve the quadratic equation (x−5)2−100=0 x=5x=5 and x=−15x=−15 x=5x=5 and x=15x=15 x=−5x=−5 and x=15x=15 x=−5x=−5 and x=−15x=−15

x = −5x = −5 and x = 15

Solve the quadratic equation x2−9x+14=0 using the quadratic formula. Correct x=−14x=−14 and x=−1x=−1 x=−2x=−2 and x=−7x=−7 x=2x=2 and x=7x=7 x=14x=14 and x=1x=1

x=2 and x=7

Solve the quadratic equation x2+10x+16=0 x=−8,−2 x=8,−2 x=−8,2 x=8,2

x=−8,−2

Which quadratic equation can be algebraically manipulated to have coefficients a=2, b=−1, and c=−3? Correct 4x2−2x=−64x2−2x=−6 x2−12x−32=0x2−12x−32=0 2x2+x−3=02x2+x−3=0 −2x2+x+3=−1−2x2+x+3=−1

x^2 − 1/2x −3/2=0

Which of the following is a perfect square trinomial? Correct x2−6x−9x2−6x−9 x2−x+1x2−x+1 x2−6x+9x2−6x+9 x2−4x2−4

x^2 − 6x + 9

Ryan mistakenly copied a quadratic equation by interchanging the coefficients bb and cc. When he solved the equation, he got x=1±√2. Which of the following is the correct quadratic equation? −x2−x−2=0−x2−x−2=0 −x2+x−2=0−x2+x−2=0 x2−x−2=0x2−x−2=0 x2−x+2=0x2−x+2=0

x^2 − x − 2 = 0

Which of the following is a quadratic equation written in standard form? -z^2 = 6z + 2 2x^2 + 4x = 5 y^2 - 3y + 4 = 0 x - 3x^2 + 5 = 0

y^2 − 3y + 4 = 0

Which of the following equations are transformable to quadratic equations? Correct y3−y6=4y3−y6=4 3z5+z2−7=03z5+z2−7=0 w2−w6−2=0w2−w6−2=0 4x2−x4−2=04x2−x4−2=0

y^3 - y^6 = 4

Which of the following can be used to solve the equation (z−6)2=2z? Correct z=−16 ±√(16)2−4(1)(36)2z=−16 ±(16)2−4(1)(36)2 z=14±√(−14)2−4(1)(36)2z=14±(−14)2−4(1)(36)2 z=16±√(−16)2−4(1)(36)2z=16±(−16)2−4(1)(36)2 z=−14±√(14)2−4(1)(36)2z=−14±(14)2−4(1)(36)2

z = 14 + √(-14)^2 -4(1)(30) / 2

Find the solution set of the quadratic equation (x+2)2+(x−1)2=0 using the quadratic formula. Correct {1±3i2}{1±3i2} {−1±6i2}{−1±6i2} {−1±3i2}{−1±3i2} {1±6i2}{1±6i2}

{ -1 + 3i / 2 }

What is the solution set of the quadratic equation (x−5)(x+1)=7? {-1, 5} {-2, 6} {6, 12} {-6, 2}

{-2, 6}

Find the solution set of the quadratic equation x2−(2x+1)2=0 using the quadratic formula. Correct {1,131,13} {−1,−13−1,−13} {0,430,43} {0,−430,−43}

{−1,−1/3}

Which is the complete solution set of y2=81? Correct {−9−9} {−9,9−9,9} no solution {99}

{−9,9}

Which of the equations have solutions that are imaginary numbers? 1+(2+x)2−4=0 −(x−3)2−7=0 −2u2+4=1 3s2+36=0

− (x−3) 2 − 7 = 0 3s^2 + 36 = 0

If 4√w+2√w=3 is transformed into a quadratic equation and u4=wu4=w, which of the following are the values of uu? Correct −3/2 1 −1 32

−3/2 1

Which of the following is a solution to the quadratic equation 3x2−15=0 2525 −√5−5 55 √1515

−√5

Solve the equation s−4−9s−2+18=0. Correct −√6/6 −√3/3 √6/6 √3/3

−√6/6 −√3/3 √6/6 √3/3

Which of the following expressions reduces to 3√3? √9 √18 √27 √6

√27