If α , β be the roots of x 2 + p x − q = 0 and γ , δ are the roots of x 2 + p x + r = 0 , q + r  = 0 , then ( β − γ ) ( β − δ ) ( α − γ ) ( α − δ ) is equal to

Question

If α , β be the roots of x 2 + p x − q = 0 and γ , δ are the roots of x 2 + p x + r = 0 , q + r  = 0 , then ( β − γ ) ( β − δ ) ( α − γ ) ( α − δ ) ​ is equal to

TestHub · Accepted Answer

Here, α + β = − p = γ + δ ​ ( α − γ ) ( α − δ ) = α 2 − α ( γ + δ ) + γ δ = α 2 − α ( α + β ) + r ​ = − α β + r = q + r ​ Similarly ( β − γ ) ( β − δ ) = q + r So, ratio is 1

Mathematics - Quadratic Equation Question with Solution | TestHub

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