Question

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

a) 4x^2 + 6x + 8
b) 4x^2 - 6x - 8
c) 4x^2 - 6x + 8
d) 4x^2 + 6x - 8

Answer 1

The quadratic equation with roots 2 and 4 and leading coefficient 4 is 4x^2 - 24x + 32 = 0.

Step-by-step explanation:

To write the quadratic equation with roots 2 and 4 and leading coefficient 4, we first need to understand the general form of a quadratic equation. A quadratic equation has the form ax^2 + bx + c = 0, where a, b, and c are constants. The roots of a quadratic equation are the values of x that make the equation equal to zero.

Since the roots are given as 2 and 4, we can write two separate equations using the roots:

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

Expanding this equation gives us:

x^2 - 6x + 8 = 0

Since our leading coefficient is 4, we can multiply every term in the equation by 4 to get:

4x^2 - 24x + 32 = 0

Therefore, the quadratic equation with roots 2 and 4 and leading coefficient 4 is: 4x^2 - 24x + 32 = 0.