SOLUTION: How would I solve: Find the values for p for which the equation; (p+3)x^2-12x+2p=0 has equal roots. Thanks.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: How would I solve: Find the values for p for which the equation; (p+3)x^2-12x+2p=0 has equal roots. Thanks.      Log On


   

Question 805355: How would I solve:
Find the values for p for which the equation;
(p+3)x^2-12x+2p=0
has equal roots.
Thanks.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
%28p%2B3%29x%5E2-12x%2B2p=0

In any quadratic equation if the roots are equal then b%5E2-4ac%29+=+0 in the equation ax%5E2%2Bbx%2Bc
compare the two equations
a=(p+3), b=-12, c=2p
b%5E2-4ac=0
(-12)^2-4(p+3)(2p)=0
144-8p^2-24p=0
Or
8p^2+24p-144=0
/8
p%5E2%2B3p-18=0
p%5E2%2B6p-3p-18=0

p(p+6)-3(p+6)=0
(p+6)(p-3)=0
p=-6 OR 3