The number of values of the parameter α∈0,2π for which the quadratic function sin⁡αx^2+2cos⁡αx+1/2cos⁡α+sin⁡α is the square of a linear function is

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Correct answer: (B) 4. For the quadratic function to be square of a linear function D=0 ⇒4cos^2⁡α-4·1/2sin⁡αcos⁡α+sin⁡α=0⇒2cos⁡α+sin⁡αcos⁡α-sin⁡α=0 ⇒tan⁡α=1 or -2 For α∈0,2π there are two solutions for each. ⇒ total four values of α.

The number of values of the parameter $α \in [0, 2 π]$ for which the quadratic function $(\sin α) x^{2} + (2 \cos α) x + \frac{1}{2} (\cos α + \sin α)$ is the square of a linear function is

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The number of values of the parameter α∈0,2π for which the quadratic function sin⁡αx2+2cos⁡αx+12cos⁡α+sin⁡α is the square of a linear function is

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More Trigonometric Equations Questions

The number of values of the parameter $α \in [0, 2 π]$ for which the quadratic function $(\sin α) x^{2} + (2 \cos α) x + \frac{1}{2} (\cos α + \sin α)$ is the square of a linear function is