Question

If $(0,b,0)$ is the centroid of the triangle formed by the points $(4,2,-3)$ , $(a,-5,1)$ and $(2,-6,2)$ . If $a,b$ are the roots of the quadratic equation $x^2+px+q=0$, then $p,q$ are

• A. $9,18$
• B. $-9,-18$
• C. $3,-18$
• D. $-3,18$

Answer 1

The correct option is A $9,18$

Since $a,b$ are the roots of the equation
$x^2+px+q=0$
$\Rightarrow a+b=-p$ and $ab=q$

Centroid of triangle is $(\frac{a+6}{3},-3,0)$
Given, centroid $(0,b,0)$

Comparing, we get $b=-3$
and $\frac{a+6}{3}=0$

$\Rightarrow a=-6$
Hence, $p=9,q=18$

Hence, option A.