Question

Find the equation given the roots -2, 1, and square root of 7

Answer 1

`x^(3)  - (√(7)  - 1)x^(2)  - (2 + √(7) )x + 2√(7) = 0`

Explanation:

We have to find the equation of a polynomial whose roots are - 2, 1 and √7.

It will be a single variable three-degree equation.

Let the variable is x.

So, (x + 2), (x - 1) and (x - √7) will be the factors of the equation.

Therefore, the equation can be written as

`(x + 2)(x - 1)(x - √(7) ) = 0`

⇒
`(x^(2)  + x - 2)(x - √(7) ) = 0`

⇒
`(x^(3)  + x^(2)  - 2x - √(7) x^(2)  - √(7) x + 2√(7) ) = 0`

⇒
`x^(3)  - (√(7)  - 1)x^(2)  - (2 + √(7) )x + 2√(7) = 0`

So, this is the required equation. (Answer)