Question

Assertion :If $\alpha ,\beta$ are roots of the equation $3x^2-11x+19=0$, then it is possible to find the value of ${\alpha }^2+{\beta }^2$. Reason: Any symmetric function of roots can be expressed in term of elementary symmetric functions $S=\alpha +\beta ,P=\alpha \beta$.

• 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. Both Assertion and Reason are incorrect

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

$3x^2-11x+19=0$
Let the roots be $\alpha ,\beta$.
Hence,
$\alpha +\beta =\frac{11}{3}$
and $\alpha .\beta =\frac{19}{3}$
Hence,
${\alpha }^2+{\beta }^2$
$=(\alpha +\beta {)}^2-2\alpha .\beta$
$=\frac{121}{9}-\frac{38}{3}$

$=\frac{121-114}{3}$
$=\frac{7}{9}$
Hence, assertion and reason are both correct and reason is the correct explanation of assertion.