Question

Write a polynomial equation with integer coefficients that has the given roots x=1, x=-4

Answer 1

(x -1)(x +4) = 0

x² +3x -4 = 0 . . . . . . probably the form you're looking for

Answer 2

Answer with Step-by-step explanation:

If a polynomial has roots a and b

Then, equation of polynomial can be given by:

(x-a)(x-b)= x²-(a+b)x+ab

Here, we are given roots of polynomial to be 1 and -4

i.e. a=1 and b= -4

Polynomial equation=x²- (1+(-4))x+1(-4)

                                  = x² - (1-4)x - 4

                                  = x² + 3x - 4

Hence, A polynomial equation with integer coefficients that has roots x=1 and  x= -4 is:

x² + 3x - 4