Question

For what value of p equation px² +6x + 4p = 0 has product of root equal to the sum of roots.

Answer 1

Let α  and  β are the roots of the quadratic equation.

Given quadratic equation is px² +6x + 4p = 0.
Product of roots =  sum of roots= α . β = α +  β

On comparing with ax² + bx + c
a= p , b= 6 , c= 4p

Product of zeroes(α.β)= c/a
α.β = 4p /p
α.β = 4

Sum of zeroes (α+β) = -b/a
α+β = -(6)/p

α . β = α +  β        ( GIVEN)
4 = -6/p
4p = -6
p = -6/4
p = -3/2

Hence, the value of p = -3/2

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Answer 2

The ans is in the clip provided

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