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Question
If one root of the equation 3x2 + kx + 81 = 0 (having real roots) is the square of the other then find k
Solution
Let α and α2 be the root of the equation 3x2 + kx + 81
Here a = 3, b = k, c = 81
α + α2 = `- "k"/3`
3α + 3α2 = – k ...(1)
Product of the roots = `"c"/"a" = 81/3` = 27
α × α2 = 27
α3 = 27 ⇒ α3 = 33
α = 3
Substitute the value of α = 3 in (1)
3(3) + 3(3)2 = – k
9 + 27 = – k
⇒ 36 = – k
∴ k = – 36
The value of k = – 36
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