Question

Assertion :If $a,b,cϵZ$ and $a{x}^2+bx+c=0$ has an irrational root, then $|f\left(\lambda \right)|\ge 1/q^2$, where $\lambda ϵ(\lambda =\frac{p}{q};p,qϵZ)$ and $f\left(x\right)=a{x}^2+bx+c$. Reason: If $a,b,cϵQ$ and $b^2-4ac$ is positive but not a perfect square, then roots of equation $a{x}^2+bx+c=0$ are irrational and always occur in conjugate pair like $2+\sqrt{3}$ and $2-\sqrt{3}$.

• 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 A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Roots of $a{x}^2+bx+c=0$
$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$
So $b^2-4ac$ will not be perfect square for irrational roots.
Thus assertion and reason both are correct and the reason is the correct explanation for the assertion.