The set of all values of

MATHEMATICS · Single correct · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

The set of all values of k>−1k > -1 , for which the equation (3x2+4x+3)2−(k+1)(3x2+4x+3)(3x2+4x+2)+k(3x2+4x+2)2=0(3x^2 + 4x + 3)^2 - (k + 1)(3x^2 + 4x + 3)(3x^2 + 4x + 2) + k(3x^2 + 4x + 2)^2 = 0 has real roots, is: (A) (1,52]\left(1, \frac{5}{2}\right] (B) [2,3)[2, 3) (C) [−12,1)\left[-\frac{1}{2}, 1\right) (D) (12,32]−{1}\left(\frac{1}{2}, \frac{3}{2}\right] - \{1\}

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