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Write the quadratic equation whose roots are −2 and −6, and whose leading coefficient is 3.

User Wu Wei
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1 Answer

4 votes

Answer:

3x² + 24x + 36 = 0

Explanation:

A quadratic equation has the standard form ax² + bx + c = 0.
a, b and c are constants.

The roots of a quadratic equation represent the two solutions to the quadratic equation

Given that the roots are -2 and -6 we have

x = -2 and x = -6 as the solutions

Add 2 to both sides of x = -2 ==> x + 2 = 0
Add 6 to both sides of x = -6 ==> x + 6= 0

So (x+2)(x+6) = 0 is the factored representation of this equation. We have to multiply by a leading coefficient of 3

So the quadratic equation is
3(x+2)(x+6) = 0


Using the FOIL method
(x + 2)(x + 6) = x² + 6x + 2x + 12 = x² + 8x + 12

The leading coefficient is the coefficient of x² and is given as 3

So the quadratic equation in standard form is
3(x² + 8x + 12) = 0

==> 3x² + 24x + 36 = 0

If you solve this equation on a quadratic equation calculator you will get the solutions x = -2 and x=-6

User Iaroslav Baranov
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5.2k points