M Munkiie Member Joined May 22, 2012 Messages 31 Gender Undisclosed HSC 2013 Feb 18, 2013 #1 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!
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!
Q qrpw Member Joined Apr 8, 2010 Messages 83 Gender Male HSC 2012 Feb 18, 2013 #2 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
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
M Munkiie Member Joined May 22, 2012 Messages 31 Gender Undisclosed HSC 2013 Feb 19, 2013 #3 Ok thanks
