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
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$9,18$
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$-9,-18$
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$3,-18$
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$-3,18$
A
Correct answer
Explanation
Centroid = ((4+a+2)/3, (2-5-6)/3, (-3+1+2)/3) = ((6+a)/3, -3, 0). Given centroid is (0, b, 0), so (6+a)/3 = 0 -> a = -6. And b = -3. The quadratic equation is x^2 + px + q = 0 with roots -6 and -3. Sum of roots = -p = -9 -> p = 9. Product of roots = q = 18.