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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.

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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

1 Answer 1

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

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

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