Question

the sum of two roots of quadratic equation is 4 sum of their cube is 35 find equation

Answer 1

(a+b)³=a³+b³+3ab(a+b)

a³+b³=(a+b)³-3ab(a+b)

let the roots of our equation are a,b

we have sum of roots

a+b= 5. (eq1)

and

a³+b³=35

AND

using the above relation we can find the product of roots of the equations.

35=(5)³-3ab(5)

35=125-15ab

15ab=90

ab=6. (eq2)

HENCE Product of the roots of the equation.

using both equations 1 and 2

the required equation with the sun of roots 5 and product of roots 6.

ANSWER x²-5x+6=0

AND ONE MORE THING IF YOU LIKE THE ANSWER DON'T FORGET TO HIT THE BRILLIANT BUTTON.

Answer 2

x+y=4

x^3+y^3=35........…