If the quadratic equation 4^ ^2 x^2 + 2x + ( ^2 - + 1 2 ) = 0 has real roots

MATHEMATICS · Subjective · CBSE · Mathematics · Quadratic Equations · Quadratic Equations

Problem

If the quadratic equation 4sec⁡2αx2+2x+(β2−β+12)=04^{\sec^2 \alpha} x^2 + 2x + \left( \beta^2 - \beta + \frac{1}{2} \right) = 0 has real roots, then find all the possible values of cos⁡α+cos⁡−1β\cos \alpha + \cos^{-1} \beta.

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