If the sum of the roots of an equation is 2 and the sum of their cubes is 98, then find the equation.

Answer

`x^(2) - 2x - 15 = 0`

Explanation

Let the roots be ` alpha and beta ` . Then ,
` alpha + beta = 2 and alpha^(3) + beta^(3) = 98`
Now, ` alpha^(3) + beta^(3) = (alpha + beta ) (alpha^(2) - alpha beta + beta^(2))`
`rArr 98 = 2 [(alpha + beta)^(2) - 3alpha beta]`
or ` 49 = (4 - 3 alpha beta)`
or ` alpha beta = - 15`
Thus, the equation is `x^(2) - 2x - 15 = 0`