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If P and Q Are the Roots of the Equation X2 − Px + Q = 0, Then - CBSE Class 10 - Mathematics

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Question

If p and q are the roots of the equation x2 − px + q = 0, then

  • p = 1, q = −2

  • p = 1, q = −2

  • p = −2, q = 0

  • p = −2, q = 1

Solution

Given that p and be the roots of the equation  x2 − px + q = 0

Then find the value of p and q.

Here, a = 1,b= -p and,c = q

p and q be the roots of the given equation

Therefore, sum of the roots

`p+q = (-b)/ a`

         `=(-p)/1`

         `=-p`

q = -p -p   

   = -2p….. (1)

Product of the roots

As we know that 

`p xx q = q/1`

        `p = q/q`

            = 1

Putting the value of p=1 in equation (1)

`q = -2 xx 1`

    = -2

Therefore, the value of  p = 1 ; q = -2 .

  Is there an error in this question or solution?

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Solution If P and Q Are the Roots of the Equation X2 − Px + Q = 0, Then Concept: Solutions of Quadratic Equations by Factorization.
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