Q7 of 46 Page 1

Find the value(s) of k so that the quadratic equation has equal roots.

We know that quadratic equation has two equal roots only when the value of discriminant is equal to zero.

Discriminant is equal to 0, is given by


b2 – 4ac = 0 …(i)


Comparing x2 – 4kx + k = 0 with general quadratic equation ax2 + bx + c = 0, we get


a = 1, b = -4k and c = k


Substituting these values in equation (i), we get


(-4k)2 – 4(1)(k) = 0


⇒ 16k2 – 4k = 0


⇒ k(16k – 4) = 0


⇒ k = 0 or 16k – 4 = 0


⇒ k = 0 or 16k = 4


⇒ k = 0 or k = 1/4


Hence, the values of k are 0 and 1/4.


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