1.4 Hw Q's Math

Solve the equation using the quadratic formula. x^2 = 6x - 25

( 3 + 4i, 3 - 4i)

Solve by factoring. 3y^2 + 16y + 20 = 0

(-2, -10/3)

Solve the equation using the quadratic formula. r^2 + 3r - 3 = 0

(-3 ± √21 /2)

Which equation is set up for direct use of the square root​ property? Choose the correct answer below and find the solution. a. x^2 + x = 6 b. (2x + 3)^2 = 3 c. (5x - 1)(x - 2) = 0 d. 5x^2 - 14x -3 = 0

(2x + 3)^2 = 3 answer: -3 ± √3 / 2

Solve the equation by using the square root property. (3p +1)^2 = 12

(2√3 -1/3, -2√3 -1/3)

Solve the equation by the​ zero-factor property. t^2 - 5t + 6 = 0

(3,2)

Which equation is set up for direct use of the​ zero-factor property? Solve it and find the solution. a. 3x^2 - 23x -8 = 0 b. (8x + 5)^2 = 3 c. x^2 + x = 132 d. (3x - 1)(x - 1) = 0

(3x - 1)(x - 1) = 0 answer: (1/3, 1)

Solve the cubic equation using factoring and the quadratic formula. x^3 - 216 = 0

(6, - 3 + 3i √3, - 3 - 3i√3)

Determine the discriminant of the quadratic equation. Use the value of the discriminant to determine whether the quadratic equation has two rational​ solutions, two irrational​ solutions, one repeated real​ solution, or two complex solutions that are not real. 5z^2 + 9z + 11 = 0

- discriminant: -139 - two complex solutions that are not real

Evaluate the discriminant for the following equation. Then use it to determine the number of distinct​ solutions, and tell whether they are​ rational, irrational, or nonreal complex numbers. 3x^2 + 4x +1 = 0

- discriminant: 4 - The equation has two distinct rational solutions.

x + 5 = 0

-5

x - 5 = 0

5

Only one of the equations is set up so that the values of​ a, b, and c can be determined immediately. Which one is​ it? Solve it and find the solution. a. (8x - 3)(x - 1) = 0 b. 8x^2 - 21x - 9 = 0 c. (4x + 5)^2 = 5 d. x^2 + x = 12

8x^2 - 21x - 9 = 0 answer: (-3/8, 3)

Solve by completing the square. x^2 - 18x -4 = 0

9 ± √85

A quadratic equations ax^2 + bx + c = 0 has 5 - √26 and 5 + √26 as solutions. Find the values of b and c if the value of a is 1. (Hint: Use the zero-factor property in reverse.)

a = 1, b = -10, c= -1

Solve the following equation for t. s = 1/6gt^2

t = ± √6sg / g

Francisco claimed that the equation x^2 − 8x = 0 cannot be solved by the quadratic formula since there is no value for c. Is he​ correct?

yes

x^2 = -28

± 2i √7

x^2 = 28

± 2√7

x^2 = 80

± 4 √5

x^2 = - 80

± 4i √5

x^2 = 25

± 5

x^2 = -25

± 5 i

x^2 = 49

± 7

x^2 = -49

± 7i

x^2 + 5 = 0

± i √5

x^2 + 7 = 0

± i √7

x^2 - 5 = 0

± √5

x^2 - 7 = 0

± √7