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
