Let $p, q$ and $r$ be real numbers $(p \ne q,r \ne 0),$ such that the roots of the equation $\frac{1}{{x + p}} + \frac{1}{{x + q}} = \frac{1}{r}$ are equal in magnitude but opposite in sign, then the sum of squares of these roots is equal to .
${p^2} + {q^2} + {r^2}$
${p^2} + {q^2}$
$2({p^2} + {q^2})$
$\frac{{{p^2} + {q^2}}}{2}$
The number of real roots of the equation $5 + |2^x - 1| = 2^x(2^x - 2)$ is
The sum of all integral values of $\mathrm{k}(\mathrm{k} \neq 0$ ) for which the equation $\frac{2}{x-1}-\frac{1}{x-2}=\frac{2}{k}$ in $x$ has no real roots, is ..... .
The number of cubic polynomials $P(x)$ satisfying $P(1)=2, P(2)=4, P(3)=6, P(4)=8$ is
The two roots of an equation ${x^3} - 9{x^2} + 14x + 24 = 0$ are in the ratio $3 : 2$. The roots will be
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