Question

Write the quadratic equation whose roots are − 1 and − 4 , and whose leading coefficient is 4 .

Answer 1

`4(x+1)(x+4)=0 \text{ or } 4x^2 +20x+16=0`

Explanation:

The quadratic equation can be written in two ways:

`ax^2 +bx+c=0`

or

`a(x-x_1)(x-x_2)=0`

where
`a` is the leading coefficient and
`x_1, x_2` are roots of the equation.

You are given

`a=4\\ \\x_1=-1\\ \\x_2=-4`

Hence, it is easier to write the quadratic equation in the second form:

`4(x-(-1))(x-(-4))=0\\ \\4(x+1)(x+4)=0`

If you myltiply all terms then the equation will be written in the first form:

`4\cdot x^2+4\cdot 4x+4\cdot x+4\cdot 1\cdot 4=0\\ \\4x^2 +20x+16=0`