C1-Algebra basics and Quadratic equations

Expand 3(x+2).

3x + 6

Solve: x^4+3x^2-4=0

Real root of x=+/-1

Derive the quadratic formula from ax^2+bx+c=0.

x=(-b+/-root(b^2-4ac)/2a

Solve 15=5x

x=3

Solve 3/x=5/(x+2).

x=3

Solve 7x-20=2x-5

x=3

Solve: 3x^2 -18x +1=0

x=3 +/-root(26/3)

Solve (8x-1)/(x+2)=5.

x=3 2/3

Solve: 2x^2-x-3=0

x=3/2 or -1

Solve 7/(5x-3)=2/(x+1).

x=4 1/3

Solve 18=6x-7

x=4 1/6

Expand -2(3a-2)(4a-1).

=-2(12a^2-3a-8a+2)=-2(12a^2-11a-3)=-24a^2+22a-4

Expand -5a(4a^2 - 2a + 1).

=-20a^3+10a^2-5a

Solve (3x/5)-2x=4.

x=-2 6/7

Solve 3=(15x+2)/4x.

x=-2/3

Solve 4-7x=x-12

x=2

Solve 5x+4=14

x=2

Solve 8/x=4.

x=2

Solve x+10=12

x=2

Solve 7=(3-4x)/(2x-5)

x=2 1/9

Solve 7-5(3x-4)=3-(2x+5)

x=29/13=2 3/13

Solve: 4+3x=x^2

x=4 or -1

Solve: x^2-8x=2

x=4+/-3root2

Solve 2x=10

x=5

Solve: 2x^2-10x-3=0

x=5/2 +/-root(31)/2

Solve: 3x^2/3 -5x^1/3 +2=0

x=8/27 or 1

Expand (5x-2)(x-2)(2x-1).

=(5x-2)(2x^2-x-4x+2)=(5x-2)(2x^2-5x+2)=10x^3-25x^2+10x-4x^2+10x-4=10x^3-29x^2+20x-4

Label the parts of:x^2-x=3x-6.

Terms: x^2, -x, 3x and -6 Expressions (2 or more terms put together): x^2-x and 3x-6 Equations: x^2-x=3x-6

An equation is...

Where an expression is not the same as another term or expression once factorised, expanded or simplified; therefore a value of x can be found e.g. x+3=7 This is expressed using the = sign.

Find the value of k for which x^2+kx+9=0 has different roots.

k<-6 or k>6

Find the value of k for which kx^2-4x+1=0 has equal roots.

k=4

Find the value of k for which x^2+6x+k=0 has no real roots.

k>9

Solve 3x^2-8x+2=0

x=(4+/-root10)/3

Solve: x^2-9=0

x=-3 or 3

Solve (3x-2)/4-(x-2)/3=(2x-1)/6.

x=-4

Solve 3(2x-1)=4(x-2).

x=-5/2=-2 1/2

Solve: 10x^2 + 5x=0

x=0 or -1/2

Solve: x^2=3x

x=0 or 3

Solve 5-3/2x=4.

x=1 1/2

Solve (4x-7)/10=(x-3)/5.

x=1/2

Solve 5-3x=4.

x=1/3

Solve 5x-3/4=x+2

x=11/16

Solve (5x-3)/4=2.

x=11/5=2 1/5

Expand (4-5x)^2.

=16-40x+25x^2

Expand (x^2+3x-2)(2x^2-1).

=2x^4-x^2+6x^3-3x-4x^2+2=2x^4+6x^3-5x^2-3x+2

Expand 5 -2(5x-3).

=5 - 10x + 6=11-10x

Expand 2(3x^2-6x-1)-(x^2-4x+2).

=6x^2-12x-2-x^2+4x-2=5x^2-8x-4

Expand (3+2x)^2.

=9+12x+4x^2

Expand (3x-5)^2.

=9x^2-30x+25

Expand (x+3)^2.

=x^2+6x+9

Expand (x+4)^2.

=x^2+8x+16

Expand (x-6)^2.

=x^2-12x+36

Expand (x+2)(x-3).

=x^2-3x+2x-6=x^2-x-6

Expand (x-3/2)^2.

=x^2-3x+9/4

A quadratic equation...

Has different roots (if discriminant is >0) Has one root (if discriminant is 0) Has no (real) roots (if discriminant is <0)

The discriminant of a quadratic equation ax^2+bx+c...

Is b^2-4ac

An identity...

Is where one expression is exactly the same as another, once expanded, simplified or factorised; so a value of x cannot be found. e.g. 3x+3 = 3(x+1)This can be expressed using a triple equals sign.

Solve 6=17-7x.

x=11/7=1 4/7

Solve x/3=4.

x=12

Solve 8=x-5

x=13

Solve x-5=8

x=13