quadratic equation whose roots are 5 and 2 , and whose leading coefficient is 4 . (Use the letter x to represent the variable

Question

Write a quadratic equation whose roots are 5 and 2 , and whose leading coefficient is 4 . (Use the letter x to represent the variable

Answer 1

If 2 and 5 are roots, then (x - 2) and (x - 5) are factors.

 

f(x) = 4(x - 2)(x - 5)               FOIL

f(x) = 4(x² - 7x + 10)             distribute

f(x) = 4x² - 28x + 40

Answer 2

To get roots of 2 and 5 the factors must be (x - 2) and (x - 5) 

to have a leading coefficient of 4, multiply product of those two factors by 4.

 

4(x - 2)(x - 5) = 4(x^2 - 7x + 10) = 4x^2 - 28x + 40