Let $\alpha$ and $\beta$ be the two disinct roots of the equation $x^3 + 3x^2 -1 = 0.$ The equation which has $(\alpha \beta )$ as its root is equal to
$x^3 -3x -1 =0$
$x^3 -3x^2 + 1 = 0$
$x^3 + x^2 -3x + 1 = 0$
$x^3 + x^2 + 3x -1 = 0$
The least integral value $\alpha $ of $x$ such that $\frac{{x - 5}}{{{x^2} + 5x - 14}} > 0$ , satisfies
If the roots of the equation $8{x^3} - 14{x^2} + 7x - 1 = 0$ are in $G.P.$, then the roots are
The product of the roots of the equation $9 x^{2}-18|x|+5=0,$ is
If $x$ be real, then the minimum value of ${x^2} - 8x + 17$ is
Let $a, b, c, d$ be real numbers between $-5$ and $5$ such that $|a|=\sqrt{4-\sqrt{5-a}},|b|=\sqrt{4+\sqrt{5-b}},|c|=\sqrt{4-\sqrt{5+c}}$ $|d|=\sqrt{4+\sqrt{5+d}}$ Then, the product $a b c d$ is