Question

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

Answer 1

Let the roots be a,b

now a+b=5 and a^3+b^3=35 (given)

a^3+b^3=(a+b)(a^2+b^2-ab)

35=5[(a+b)^2-3ab]

7=25-3ab

3ab=18 and ab=6

from this the quadratic equation is, x^2-5x+6=0

Hope this helps