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Quadratic Equation and Inequalities question

2022 · 26 Jul · Shift 1 · Q39
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  5. /2022 · 26 Jul · Shift 1 · Q39

Quadratic Equation and Inequalities question

2022 · 26 Jul · Shift 1 · Q39

JEE MainMathematicsQuadratic Equation and InequalitiesNumerical+4 / −1
If for some p,q,r∈R\mathrm{p}, \mathrm{q}, \mathrm{r} \in \mathbf{R}p,q,r∈R, not all have same sign, one of the roots of the equation (p2+q2)x2−2q(p+r)x+q2+r2=0\left(\mathrm{p}^{2}+\mathrm{q}^{2}\right) x^{2}-2 \mathrm{q}(\mathrm{p}+\mathrm{r}) x+\mathrm{q}^{2}+\mathrm{r}^{2}=0(p2+q2)x2−2q(p+r)x+q2+r2=0 is also a root of the equation x2+2x−8=0x^{2}+2 x-8=0x2+2x−8=0, then q2+r2p2\frac{\mathrm{q}^{2}+\mathrm{r}^{2}}{\mathrm{p}^{2}}p2q2+r2​ is equal to ‾\underline{\hspace{2cm}}​,
Numerical answer
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