Question

What are the zeros is the equation m^3 - 9m + 8 = 0

Answer 1

Answer:
`1,(-1+√(33) )/(2) ,(-1-√(33) )/(2)`

Explanation:

Zeros of a equation are the solutions to the equation when its value becomes zero.

Given
`m^(3)-9m+8=0`

This is a cubic equation,so first guess a root.

Try trail and error with common roots like
`1,0,-1,2...`

The given equation is satisfied when
`1` is tried.

So,
`1` is a root of the given equation.

`m-1` is factor of the equation.

Divide the given equation with the obtained factor to get a quadratic equation.

`(m^(3)-9m+8)/(m-1)=m^(2)+m-8`

The roots of the above quadratic equation can be obtained by the formula

`\frac{-b+\sqrt{b^(2)-4ac}}{2a}`,
`\frac{-b-\sqrt{b^(2)-4ac}}{2a}`

Substituting gives,

`(-1+√(33) )/(2) ,(-1-√(33) )/(2)`