Question

lf the roots of the equation $(a^2-bc)$ $x^2+2(b^2-ca)x+(c^2-ab)=0$ are equal, then the condition is

• A. $a+b+c=0$
• B. $a^3+b^3+c^3-3abc=0$
• C. $a=0$ or $a^3+b^3+c^3-3abc=0$
• D. $b=0$ or $a^3+b^3+c^3-3abc=0$

Answer 1

The correct option is D $b=0$ or $a^3+b^3+c^3-3abc=0$

Condition for roots of a quadratic equation to be equal is $b^2=4ac$
$\Rightarrow (b^2-ca{)}^2=(c^2-ab\left)\right(a^2-bc)$
$b^4+c^2{a}^2-2a{b}^{2}c=c^2{a}^2-a^{3}b+a{b}^{2}c-b{c}^3$
$b(a^3+b^3+c^3-3abc)=0$
$\Rightarrow b=0or{a}^3+b^3+c^3=3abc$