Question

ots
Find the quadratic equation for which sum of
the roots is 7 and the sum of the squares of the
roots is 25.​

Answer 1

Answer:

x+y=7

×^2+y^2 = 25

(x+y)^2 = x^2+y^2+2xy

7^2= 25 ^2 + 2xy

49 =625 + 2xy

-2xy = 49-625

-2xy = - 576

xy = 288

Therefore the quardratic equation will be

x^2- 7x +288

(according to the formula)

Hope it helps!!!!

Answer 2

Answer:

The quadratiic equation is x^2 -7x + 12

Step-by-step explanation:

let the roots of the quadratic equation be a & b

Then the quadratic equation will be in the form ,

x^2 - (a+b)x + ab = 0

given , a + b = 7 ------(1)

and a^2 + b^2 = 25 ------(2)

squaring equation(1) on both sides ,

=> (a+b)^2 = (7)^2

[ (a+b)^2 = a^2 + b^2 + 2ab ]

=> a^2 + b^2 + 2ab = 49

=> 25 + 2ab = 49 [ ∵ from eq(2) ]

=> 2ab = 49 - 25 = 24

=> ab = 12

we have ab = 12 and a+b = 7 so the quadratic

equation is , x^2 - 7x + 12

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