Question

write the quadratic equation whose roots are 5 and -6, and whose leading coefficient is 2.
(use the letter \\(x\\) to represent the variable.)

\\\box = 0\\

Explanation:

Set up the factored form of the quadratic equation

$$ a(x - r_1)(x - r_2) = 0 $$

$$ a = 2,\quad r_1 = 5,\quad r_2 = -6 $$

Substitute the given values into the equation

$$ 2(x - 5)(x - (-6)) = 0 $$

$$ 2(x - 5)(x + 6) = 0 $$

Expand and simplify the expression

$$ 2(x^2 + 6x - 5x - 30) = 0 $$

$$ 2(x^2 + x - 30) = 0 $$

$$ 2x^2 + 2x - 60 = 0 $$

Answer:

Write the quadratic equation whose roots are 5 and \(-6\), and whose leading coefficient is 2.

(Use the letter \(x\) to represent the variable.)

<blank>\(2x^2+2x-60\)</blank> \(= 0\)