Question

write the quadratic equation whose roots are -2 and 4, and whose leading coefficient is 1. (use the letter x to represent the variable.) \\(\square = 0\\)

Explanation:

Step1: Use root form of quadratic

If $r_1$ and $r_2$ are roots, the equation is $(x-r_1)(x-r_2)=0$. Substitute $r_1=-2$, $r_2=4$:
$(x-(-2))(x-4)=0$ or $(x+2)(x-4)=0$

Step2: Expand the binomials

Multiply using FOIL method:
$x\cdot x + x\cdot(-4) + 2\cdot x + 2\cdot(-4)=0$

Step3: Simplify the expression

Combine like terms:
$x^2 -4x +2x -8=0$
$x^2 -2x -8=0$

Answer:

$x^2 - 2x - 8$