Question

Assertion :If equation $a{x}^2+bx+c=0;(a,b,c\in R)$ and $2x^2+3x+4=0$ have a common root, then $a:b:c=2:3:4$ Reason: If $p+iq$ is one root of the quadratic equation with real coefficients then $p-iq$ will be the other root ; $(p,q\in R,i=\sqrt{-1})$

• 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

Assertion:

Given, $a{x}^2+bx+c=0,2x^2+3x+4=0$ have a root in common.

Roots of $2x^2+3x+4=0$ are $\frac{-3\pm i\sqrt{23}}{4}$

$\therefore$ roots of $2x^2+3x+4=0$ are complex.

$\therefore$Common root is also a complex.

$a,b,cϵR\therefore$ If one root is complex, then other root is conjugate of that complex root.

$\therefore$Both roots of both equations are same.

$\therefore a:b:c=2:3:4$

Assertion is true.

Reason:

It is true that if one root is $p+iq$ for a quadratic equation with real co efficients then its conjugate $p-iq$ will be other root.$(p,qϵR)$

Reason is true and correct explanation to assertion.