Question

Assertion :If $a+b+c>0$, $a<0<b<c$, then roots of the equation $a(x-b)(x-c)+b(x-c)(x-a)+c(x-a)(x-b)=0$ are real. Reason: Roots of the equation $A{x}^2+Bx+K=0$ are real if $B^2-4AK>0$.

• 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

Given equation can be written as

$(a+b+c)x^2-(ab+bc+ca)x+3=0$

$\therefore D=4(ab+bc+ca{)}^2-12abc(a+b+c)>0$ as $abc<0,a+b+c>0$

$\Rightarrow$ Roots of the equation are real.