Question

the sum of roots of quadratic equation is 5 and sum of their cubes is 35 find the equation

Answer 1

Step-by-step explanation:

let the two roots be x and y .

so, x+y = 5

and,x^3 +y^3 = 35

=> (x+y)^3 - 3x^2y -3xy^2 = 35

=> (5)^3 - 3xy(x+y) = 35

=> 125-3xy × 5 = 35

=> 125-15xy = 35

=> xy = 90/15 = 6

=>y = 6/x

putting y in x+y = 5, we get,

x+6/x = 5

x^2 +6 =5x

x^2-5x+6 =0

(x-3)(x-2) = 0, by solving the eqn.

so ,x = 3 or x = 2 .so y = 6/3 = 2

now we have the two roots as 3 and 2.

now,

let the equation be ax^2 +bx +c

so,x+y = -b/a

3+2 = -b/a

5. = -b/a

and, x×y = c/a

3×2 = c/ a

6 = c/a

so,a = 1,b = -5 and c= 6.

so the quadratic eqn.is x^2 - 5x +6.

(answer)

Answer 2

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