Roots and coefficients of polynomials (1 Viewer)

[Munkiie]

I need help with this question... I can't seem to get it right

Two roots of x^3+mx^2+15x-7=0 are equal and rational. Find m.

Thanks in advance!

 

[qrpw]

This polynomial has a double root and one other.

x^3 + mx^2 + 15x - 7 = (x-a)^2 (x-b)
= (x^2-2ax+a^2)(x-b)

Now comparing coefficients.

b+2a=m
a^2 + 2ab = 15
(a^2)b= -7

Solving the last two, you'll get a=-1 b=-7 in about 3 lines of working (it's just algebra).
So m = b + 2a = -9

 

[Munkiie]

Ok thanks