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Find the equation for which the sum of the roots is 7 and the sum of the squares of the roots is 25...answer it fast please |
Answer» Given :
Let the roots of the equation be α, β Sum of roots = α + β = 7 Sum of squares of roots = α² + β² = 25 Using IDENTITY ( α + β )² = α² + β² + 2αβ => 7² = 25 + 2αβ => 49 - 25 = 2αβ => 24 = 2αβ => αβ = 24 / 2 = 12 General form of QUADRATIC equation - => x² - ( α + β )x + αβ = 0 [ Where α, β are the roots of the equation ] => x² - 7x + 12 = 0 Therefore the required equation is x² - 7x + 12 = 0. |
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