Question

Assertion :Let $a,b,c$ be real such that $a{x}^2+bx+c=0$ and $x^2+x+1=0$ have a common root.

$a=b=c$

Reason: Two quadratic equations with real coefficients cannot have only one imaginary root common.

• 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

Given,
$a{x}^2+bx+c=0$ and $x^2+x+1=0$ have a common root.
$\omega$ and ${\omega }^2$ are the roots of the equation,
$x^2+x+1=0$
i.e., Roots are imaginary.
But $a,b,c$ are real. Two quadratic equations with real coefficients cannot have only one imaginary root common.
So, both the roots will be in common. The equations are identical.
$\frac{a}{1}=\frac{b}{1}=\frac{c}{1}$
So, assertion is true and reason is correct explanation.
Hence, option 'A' is correct.