Let α=x∈Rmax82sin3x⋅44cos3x and β=x∈Rmin82sin3x⋅44cos3x. If 8x2+bx+c=0 is a quadratic equation whose roots are α1/5 and β1/5, then the value of c−b is equal to :
Held on 27 Jul 2021 · Verified 6 Jul 2026.
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If the roots of x² - 5x + k = 0 are in the ratio 2:3, then k equals:
Let $\alpha = 3+4+8+9+13+14+\ldots$ upto 40 terms. If $(\tan\beta)^{\frac{\alpha}{1020}}$ is a root of the equation $x^2+x-2=0$, $\beta \in \left(0, \dfrac{\pi}{2}\right)$, then $\sin^2\beta + 3\cos^2\beta$ is equal to:
If the set of all solutions of $|x^2 + x - 9| = |x| + |x^2 - 9|$ is $[\alpha, \beta] \cup [\gamma, \infty)$, then $(\alpha^2 + \beta^2 + \gamma^2)$ is equal to:
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