Question

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Two numbers p and q are such that the equation px²+3x+2q=0 has -6 as the sum of the roots and as the product of the roots. Find the value of p and q.

Answer 1

Solution:

We know that,

Sum of roots = -b/a

&, product of roots = c/a

Here, a = p , b = 3 and c = 2q

∵ Let, α and β be the roots of equation.

α + β = $\frac{-3}{p} = -6$= -6

=> p = 1/2

Also, αβ = c/a = 2q/p = -6

=> $\frac{2q}{\frac{1}{2} } = -6$ ....[p = 1/2]

=>  4q = -6

=>  q = -3/2

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