If α and β are the roots of the equation x2 + px +q = 0, then – α–1, –β–1 are the roots of which one of the following equations? यदि समीकरण x2 + px +q = 0 के मूल α और β हैं, तो निम्नलिखित समीकरणों में से किस समीकरण के मूल्य – α–1, –β–1 हैं?
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qx2 – px + 1 = 0
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qx2 + px + 1 = 0
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x2 + px – q = 0
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x2 – px + q = 0
A
Correct answer
Explanation
If α and β are roots of x^2 + px + q = 0, then sum of roots = α + β = -p and product = αβ = q. For the transformed roots -1/α and -1/β, the new sum = -(1/α + 1/β) = -(α+β)/(αβ) = p/q and new product = 1/(αβ) = 1/q. The required equation is x^2 - (sum)x + (product) = 0, which gives x^2 - (p/q)x + (1/q) = 0. Multiplying by q: qx^2 - px + 1 = 0. Option B has the wrong sign for the px term.