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Let $(α_{1}, α_{2} and β_{1}, β_{2} be the roots of a x^{2} + b x + c = 0 and p x^{2} = q x = 0$ respectively . If the system of equation $α_{1} y + α_{2} z = 0 and β_{1} y + β_{2} z = 0$ has a non- trival solution then prove that $b^{2} p r = q^{2} a c .$

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Let

(α_{1}, α_{2} and β_{1}, β_{2} be the roots of a x^{2} + b x + c = 0 and p x^{2} = q x = 0

respectively . If the system of equation

α_{1} y + α_{2} z = 0 and β_{1} y + β_{2} z = 0

has a non- trival solution then prove that

b^{2} p r = q^{2} a c .

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Question Text

Let

(α_{1}, α_{2} and β_{1}, β_{2} be the roots of a x^{2} + b x + c = 0 and p x^{2} = q x = 0

respectively . If the system of equation

α_{1} y + α_{2} z = 0 and β_{1} y + β_{2} z = 0

has a non- trival solution then prove that

b^{2} p r = q^{2} a c .

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