Given a quadratic equation x2-px-q -0-Find p-q so that the roots of the equation are p-q-

Given: p and q are the roots of the equationx2 + px + q = 0⇒sum of roots = – p⇒ p + q = – p⇒ 2p = – qand product of roots = q⇒ pq = q⇒ p = 1So q = – 2Hence, p = ...

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Standard XII

Mathematics

Relation between Roots and Coefficients for Quadratic

Given a quadr...

Question

Given a quadratic equation x²+px+q =0.Find p,q so that the roots of the equation are p,q.

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Solution

Given: p and q are the roots of the equation
x² + px + q = 0
⇒sum of roots = – p
⇒ p + q = – p
⇒ 2p = – q
and product of roots = q
⇒ pq = q
⇒ p = 1
So q = – 2
Hence, p = 1, q = – 2

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Given a quadratic equation x2+px+q =0.Find p,q so that the roots of the equation are p,q.

Given: p and q are the roots of the equationx2 + px + q = 0⇒sum of roots = – p⇒ p + q = – p⇒ 2p = – qand product of roots = q⇒ pq = q⇒ p = 1So q = – 2Hence, p = 1, q = – 2

Given a quadratic equation x²+px+q =0.Find p,q so that the roots of the equation are p,q.

Given: p and q are the roots of the equation
x² + px + q = 0
⇒sum of roots = – p
⇒ p + q = – p
⇒ 2p = – q
and product of roots = q
⇒ pq = q
⇒ p = 1
So q = – 2
Hence, p = 1, q = – 2