Question

Assertion :If the roots of $x^5-40x^4+P{x}^3+Q{x}^2+Rx+S=0$ are in G.P. and the sum of their reciprocal is 10, then $|S|=64$. Reason: $x_1{x}_2{x}_3{x}_4{x}_5=-S$, where $x_1,x_2,x_3,x_4,x_5$ are the roots of given equations.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is D Assertion is incorrect but Reason is correct

$Supposetherootsare\frac{a}{r^2},\frac{a}{r},a,ar,a{r}^{2}SoS=a^{5}and\frac{a}{r^2}+\frac{a}{r}+a+ar+a{r}^2=40Sumofreciprocalsare10\frac{1}{a}\left(\frac{40}{a}\right)=10a=\pm 2So\left|S\right|=32$