Question

Assertion :If the equation $a{x}^2+bx+c=0,(a,b,c\in R,a\ne 0)$ and $x^2+2x+3=0$ have a common root , then $a:b:c$ is $1:2:3$. Reason: The roots of the equation $x^2+2x+3=0$ are imaginary.

• 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 B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

Reason; $x^2+2x+3=0$

$\Rightarrow x=\frac{2\pm \sqrt{4-3\times 4}}{2}=\frac{-2\pm \sqrt{-8}}{2}=\frac{-2\pm 12\sqrt{2}}{2}$

Hence roots are imaginary

Assertion :

Given equations are

$x^2+2x+3=0$ ...(1)

and ${ax}^2+bx+c=0$ ...(2)

Since, Eq. (1) has imaginary roots so, Eq. (2) will also have both roots same as Eq. (1).

Thus, $\frac{a}{1}=\frac{b}{2}=\frac{c}{3}$

Hence, $a:b:c$ is $1:2:3$