Question

Write the quadratic equation whose roots are 2 and -2, and whose leading coefficient is 4

Answer 1

Answer:

$4x^2-16=0$

Step-by-step explanation:

We want to write the quadratic equation whose roots are 2 and -2, and whose leading coefficient is 4.

Since 2 and -2 are roots,   $x+2\\and\\x-2$  are factors of this quadratic function.

The factored form is given as: $a(x-2)(x+2)=0$

Since the leading coefficient is 4, a=4

Therefore the equation becomes:

$4(x-2)(x+2)=0$

Recognize and expand using difference two squares.

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

The required equation is:

$4x^2-16=0$