Question

(a) What is the value of k for which the quadratic equation 3x2 - Kx+k=0 has
equal roots?
(A) 6
(C) -12 (D) 12​

Answer 1

Answer : (D) 12 ✔✔

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Solution :

Let, the roots be

$\alpha \: and \: \beta$

Now, according to the question :

$\alpha + \beta = \frac{ - b}{a} = \frac{ - ( - k)}{3} \\ \\ = > \alpha + \alpha = \frac{k}{3} \\ \\ = > 2 \alpha = \frac{k}{3} = > \alpha = \frac{k}{6} ...(1)$

$\alpha \times \beta = \frac{c}{a} = \frac{k}{3} \\ \\ = > \alpha \times \alpha = \frac{k}{3} \\ \\ = > { \alpha }^{2} = \frac{k}{3}$

From equation (1) :

${( \frac{k}{6}) }^{2} = \frac{k}{3} \\ \\ = > \frac{ {k}^{2} }{36} = \frac{k}{3} \\ \\ = > k = \frac{36}{3} = 12$