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#### CaptainBlack

##### Well-known member
CrazyCat's Question:
"Find the discrimnant of $$kx^2 - 4x + k$$ in terms of $$k$$, hence find possible values of $$k$$ given that $$kx^2 -4x + k = 0$$ has equal roots."

For a quadratic $$ax^2+bx+c$$ the discriminant is $$b^2-4ac$$ this is the term that appears under the square root sign in the quadratic formula:
$x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}$for the solution of $$ax^2+bx+c=0$$. The quadratic equation has equal roots precisely when the discriminant is zero.
Now for the problem at hand $$a=k$$, $$b=-4$$ and $$c=k$$ so the discriminant is $$D=b^2-4ac=16-4k^2$$, and when $$D=0$$ we have $$16-4k^2=0$$ which we may solve for $$k$$ to find: $$k=\pm2$$.