Question

Write a quadratic equation that has integer coefficients and has solutions 4 and 7

Answer 1

The quadratic equation is:
`x^2-11x+28=0\\`

Explanation:

The quadratic equation with given solutions
`a` and
`b` can be written as:

`(x-a)(x-b)=0`

Given:

Solutions are 4 and 7.

The quadratic equation can be written as:

`(x-4)(x-7)=0\\`

We simplify it further to get it in standard form.

Using FOIL(Firsts Outsides Insides Lasts )

`(x* x)+(x*(-7))+((-4)* x)+(-4*(-7))=0\\\\x^2-7x-4x+28=0\\`

Combining like terms:

`x^2-11x+28=0\\`

The quadratic equation is:
`x^2-11x+28=0\\`