Question

Decide which part of the quadratic formula tells you whether the quadratic equation can be solved by factoring.

−b b^2 − 4ac 2a

Use the part of the quadratic formula that you chose above and find its value, given the following quadratic equation:

2x^2 + 7x + 3 = 0

Answer 1

a)
`b^2-4ac`

b) 25

Explanation:

a) The quadratic formula is
`x=(-b\pm √(b^2-4ac) )/(2a)`.

The portion under the radical sign (
`b^2-4ac`) is called the discriminant or determinant.

It tells us that, the quadratic equation can be solved by factoring, if its value is a perfect square.

b) The given quadratic equation is
`2x^2+7x+3=0`.

By comparing to
`ax^2+bx+c=0`, we have a=2, b=7, and c=3

We substitute these values to get:

`b^2-4ac=7^2-4(2)(3)`

`b^2-4ac=49-24`

`b^2-4ac=25`