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+Cisequalto2-(12x-(f(x) + 64x) = 0 is twice of other, then find the maximum value of theIf one root of the equation tfunction f(x), where x eR. |
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Answer» Given quadratic equation: t² − 12xt − (f(x) + 64x)=0roots are: (12x±√(144x²+4f(x)+64×4x))/2±2√(36x²+f(x)+64x)/2 =6x±√(36x²+f(x)+64x)as one root is twice the other, or f(x)=-32x²-64xHere, f(x) is a quadratic equation with D ≧ 0 and aSo the maximum value at x = -b/2a = 64/(2×-32) = -1∴ The maximum value of f(x )= f(-1) = -32(-1)² - 64(-1) = 32 (Ans) |
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