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CaptainBlack
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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."
Answer:
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: \(k=\pm2\).
CB
"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."
Answer:
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: \(k=\pm2\).
CB
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