Q10 of 227 Page 114

If one root of the equation 3x2 + kx – 81 = 0 is the square of the other, find k.

Two roots of any quadratic equation are α and β.


Here, one root is square of the other i.e α = β2


3x2 – kx – 81 = 0 compare this with ax2 – bx + c = 0


∴ a = 3, b = –k and c = –81










αβ = –27


β2(β) = –27


β3 = –27


β3 = (–3)3


β = –3


now, we are going to apply in first equation



⇒


⇒


⇒


⇒ 6 × 3 = k


⇒ k = 18


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