Question

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

Answer 1

Hey

Here is your answer,

Let the roots of our equation are a,b

we have sum of roots
a+b= 5. (eq1)

a³+b³=35

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

Hope it helps you!

Answer 2

I hope this answer is useful.
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