If α,β are the roots of the equation x2−3x+5=0 and γ,δ are the roots of the equation x2+5x−3=0, then the equation whose roots are αγ+βδ and αδ+βγ is

# If $\mathrm{\alpha },\mathrm{\beta }$ are the roots of the equation ${\mathrm{x}}^{2}-3\mathrm{x}+5=0$ and $\mathrm{\gamma },\mathrm{\delta }$ are the roots of the equation ${\mathrm{x}}^{2}+5\mathrm{x}-3=0$, then the equation whose roots are  is

1. A

${\mathrm{x}}^{2}-15\mathrm{x}-158=0$

2. B

${\mathrm{x}}^{2}+15\mathrm{x}-158=0$

3. C

${\mathrm{x}}^{2}-15\mathrm{x}+158=0$

4. D

${\mathrm{x}}^{2}+15\mathrm{x}+158=0$

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### Solution:

$\because \mathrm{\alpha }+\mathrm{\beta }=3,\mathrm{\alpha \beta }=5,\mathrm{\gamma }+\mathrm{\delta }=\left(-5\right),\mathrm{\gamma \delta }=\left(-3\right)$

Sum of roots

Product of roots

Required equation is ${\mathrm{x}}^{2}+15\mathrm{x}+158=0$  Register to Get Free Mock Test and Study Material

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