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If α and β are the roots of the equation ax2 + bx + c = 0 then the value of 1/α2 + 1/β2 is: 1. (a2 - 2cb)c22. (b2 – 2ca)/c23. (b2 + 2ca)/c24. (a2 + 2bc)/c2 |
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Answer» Correct Answer - Option 2 : (b2 – 2ca)/c2 Given: Our given quadratic equation is ax2 + bx + c = 0 Concept used: General quadratic equation in terms of roots is x2 – (α + β)x + αβ = 0 Formula used: a2 + b2 = (a + b)2 – 2ab Calculation: By comparing given quadratic equation with general quadratic equation, we get (α + β) = –b/a and αβ = c/a Now, 1/α2 + 1/β2 ⇒ (α2 + β2)/(α2β2) ⇒ ((–b/a)2 – 2(c/a))/(c/a)2 ⇒ (b2 – 2ca)/c2 ∴ The required value of given expression is (b2 – 2ca)/c2 |
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