Question

Write a quadratic equation given the roots are -2 and -1 and the leading coefficientis 2

Answer 1

The quadratic equation is
`f(x) = 2x^2 + 6x + 4`

Explanation:

Zeros of a function:

Given a polynomial f(x), this polynomial has roots
`x_(1), x_(2), x_(n)` such that it can be written as:
`a(x - x_(1))*(x - x_(2))*...*(x-x_n)`, in which a is the leading coefficient.

Roots are -2 and -1 and the leading coefficient 2

This means that
`x_1 = -2, x_2 = -1, a = 2`

So

`f(x) = 2(x - (-2))(x - (-1)) = 2(x + 2)(x + 1) = 2(x^2 + 2x + x + 2) = 2(x^2 + 3x + 2) = 2x^2 + 6x + 4`

The quadratic equation is
`f(x) = 2x^2 + 6x + 4`