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Question
Find the value of k for which the given equation has real roots:
9x2 + 3kx + 4 = 0.
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Solution
The given quadratic equation is:
9x2 + 3kx + 4 = 0
Here, a = 9, b = 3k and c = 4.
This equation has real roots if
Calculate the discriminant D of the given equation as follows:
D = b2 − 4ac
⇒ (3k)2 − (4 x 9 x 4)
⇒ 9k2 − 144
Since the given equation has equal roots, the discriminant must be equal to zero.
D = 0
⇒ 9k2 − 144 = 0
⇒ 9k2 = 144
⇒ k2 = `(144)/(9)`
⇒ k = `sqrt((144)/(9))`
⇒ k = ± 4
Hence, the required value is k = 4 and k = −4.
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