Question

Assertion :Let $\alpha ,\beta$ are roots of $f\left(x\right)=3x^2-4x+5=0.$ The equation whose roots are $2\alpha ,2\beta$ is given by $3x^2+8x-20=0$. Reason: To obtain the equation having roots $2\alpha ,2\beta$ from the equation $f\left(x\right)=0$ having roots $\alpha ,\beta$, one needs to replace $x$ with $\frac{x}{2}$ in $f\left(x\right)=0$.

• 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 incorrect but Reason is correct
• D. Both Assertion and Reason are incorrect

Answer 1

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

$\alpha +\beta =\frac{4}{3}$
And
$\alpha .\beta =\frac{5}{3}$
Hence
If the roots are $2\alpha ,2\beta$, then
$(x-2\alpha )(x-2\beta )=0$
Or
$x^2-2(\alpha +\beta )x+4\alpha .\beta =0$
Or
$x^2-\frac{8}{3}x+\frac{20}{3}=0$
Or
$3x^2-8x+20=0$