Question

For an equation $x^3-x^2-6x+6=0$, what is the value of $\sum a^2$, if $a,b,c$ are its roots ?

• A. $13$
• B. $14$
• C. $15$
• D. $16$

Answer 1

The correct option is A $13$

Given equation is $x^3-x^2-6x+6=0$
$a,b,c$ are its roots.
From the relation between roots and coefficients of a polynomial equation, we have
$a+b+c=1,ab+bc+ca=-6,abc=-6$

Using the identity,
$(a+b+c{)}^2=a^2+b^2+c^2+2(ab+bc+ca)$
$\text{Put the values of}a+b+c\text{and}ab+bc+ca$
$\Rightarrow 1^2=a^2+b^2+c^2+2\times (-6)$
$\Rightarrow 1+12=a^2+b^2+c^2$
$\Rightarrow a^2+b^2+c^2=13$