Question

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 1

Given :

• Sum of root = 7

• Sum of squares of roots = 25

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.