Quadratic Equations Algebra 1

Question

Write the quadratic equation whose roots are 2, and 4 and whose leading coefficient is 3.

Answer 1

Hi Thomas,

If 2 and 4 are roots of the quadratic equation, then x-2 and x-4 must be factors of the equation . . . because when solving a factored equation, we would set each factor equal to 0.

x - 2 = 0 means that x = 2; and

x - 4 = 0 means that x = 4.

So, the quadratic equation must be:

f(x) = (x - 2)(x - 4)

f(x) = x^2 - 6x + 8

Now, if the leading coefficient is 3, then we simply need to multiply the whole equation by 3

f(x) = 3x^2 - 18x + 24

which has a factored form that is

f(x) = 3(x - 2)(x - 4)

Hope this helps!

JMJ