3. Write an equation in which the quadratic expression 2x^2-2x-12 equals 0. Show the expression in factored form and explain what your solutions mean for the equation. Show your work.

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dhiab dhiab · Answer 1 · 2019-02-08T06:19:27+01:00

Answer:

Step-by-step explanation:

2x²-2x-12 = 2 (x²-x - 6)

but : x²-x - 6 = x² - 2(1/2)x +(1/2)² - (1/2)² - 6

= ( x - 1/2)² - 1/4 - 6

= ( x - 1/2)² - 25/4

x²-x - 6 = ( x - 1/2)² - (5/2)²

by identity ; a² - b² = (a - b ) ( a +b)

x²-x - 6 = ( x - 1/2 - 5/2) ( x - 1/2 +5/2)

x²-x - 6 = (x - 3) (x +2)

so : 2x²-2x-12 =2(x - 3) (x +2) = (2x-6)(x+2) .......(factored form)

now : 2x²-2x-12 = 0 : 2x - 6 = 0 or x+2 = 0

x= 3 or x = - 2 two solutions

MrRoyal MrRoyal · Answer 2 · 2022-02-25T12:16:10+01:00

Quadratic expressions are expressions with a power of 2

The factored expression of [tex]2x^2 - 2x - 12 = 0[/tex] is [tex]2(x+2 )(x - 3) = 0[/tex]

The expression is given as:

[tex]2x^2 - 2x - 12 = 0[/tex]

Factor out 2 in the expression

[tex]2(x^2 - x - 6) = 0[/tex]

Expand the expression

[tex]2(x^2 - 3x + 2x - 6) = 0[/tex]

Factorize the expression

[tex]2(x(x- 3) + 2(x - 3)) = 0[/tex]

Factor out x - 3

[tex]2(x+2 )(x - 3) = 0[/tex]

Hence, the factored expression of [tex]2x^2 - 2x - 12 = 0[/tex] is [tex]2(x+2 )(x - 3) = 0[/tex]

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