The possible values of k for which the quadratic

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Solution

Q.
The possible values of k for which the quadratic equation $9 x ² - 3 k x + k = 0$ has real and distinct roots:

(i) 2 (ii) 0 (iii) 5 (iv) 6

Choose the correct option from the following

1 (i) and (ii)

2 (iii) and (iv)

3 (i), (ii) and (iii)

4 (i), (iii) and (iv)

Ans.
(2)

For real and distinct roots, the discriminant (D) of the equation 9 $x ² - 3 k x + k = 0$ must be greater than zero.

$D = (- 3 k) ² - 4 \times 9 \times k > 0 \Rightarrow 9 k ² - 36 k > 0 \Rightarrow 9 k (k - 4) > 0$

This inequality implies that k < 0 or k > 4.
Therefore, the possible values of k are (iii) and (iv).

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