Question

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

(Use the letter to represent the variable.)

Answer 1

The roots occur when x is set to 0, or when they cross the x-axis.

To write the equation, we look at our roots:

x= 2
x= 4

Set these equal to 0:

x-2=0
x-4=0

These are your x factors, which can be written as:

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

To add a leading coefficient, simply multiply this equation by 4:

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

Multiply this to get a new set of factors:

(4x-8)(x-4)=0

Now use the FOIL method to obtain a quadratic equation:

4x^2 - 16x - 8x + 32 = 0

Combine like terms:

4x^2 - 24x + 32 = 0

Hope this helped!