Question

Write the polynomial equation of the least degree with roots as -2, 5 and 7.

Answer 1

Given:

The given roots are -2, 5, and 7.

To find: Write the polynomial equation of the least degree with roots -2, 5 and 7?

Step-by-step explanation:

We have given that

Given roots of polynomial equation are -2, 5, and 7.

The least degree polynomial equation will be

`(x+2).(x-5).(x-7)=0`

We solve the above expression we get,

`\begin{gathered} (x^2-5x+2x-10).(x-7)=0 \\ \\ (x^2-3x-10).(x-7)=0 \\ \\ x^3-7x^2-3x^2+21x-10x+70=0 \\ \\ x^3-10x^2+11x+70=0 \end{gathered}`

Hence, the least degree polynomial equation is x^3-10x^2+11x+70 = 0.

Answer: The least degree polynomial equation is x^3-10x^2+11x+70 = 0.