Question

write the quadratic equation whose roots are 4 and \\(-3\\), and whose leading coefficient is 4.

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

\\(\box = 0\\)

Explanation:

Set up the factored form of the quadratic equation

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

$$ a = 4,\quad r_1 = 4,\quad r_2 = -3 $$

Substitute the given values into the equation

$$ 4(x - 4)(x - (-3)) = 0 $$

$$ 4(x - 4)(x + 3) = 0 $$

Expand the expression to standard form

$$ 4(x^2 - x - 12) = 0 $$

$$ 4x^2 - 4x - 48 = 0 $$

Answer:

Write the quadratic equation whose roots are 4 and \(-3\), and whose leading coefficient is 4.

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

<blank>\(4x^2 - 4x - 48\)</blank> \(= 0\)