Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I've had some trouble with this question:

"$P(x)$ denotes the quadratic polynomial $kx^2+(k-1)x-(2k-1)$, where $k$ is a rational, real number. Find the value of $k$ for which the roots of $P(x)=0$ are equal."

How do I approach this? Any help would be appreciated.

share|cite|improve this question
Hint: value required for the discriminant? – Raymond Manzoni May 19 '13 at 11:34
Hint: What are the roots of $Ax^2+Bx+C$ if $A\ne 0$? (And what about $A=0$?) – Hagen von Eitzen May 19 '13 at 11:38

for a quadratic poly. ($ax^2+bx+c\,$) roots are equal when $b^2-4ac=0$

so in ques. $$(k-1)^2+4\cdot k\cdot (2k-1)=0$$ $$k^2+1-2k+8k^2-4k=0$$ $$9k^2-6k+1=0$$ $$9k^2-3k-3k+1=0$$ $$3k(3k-1)-1(3k-1)=0$$ $$(3k-1)^2=0$$ $$3k-1=0$$ $$k=\dfrac13$$

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.