Question

What is the discriminant of `2x^2 + x - 1 = 0` and what does that mean?

Answer 1

Solve 2x^2 + x - 1 = 0

Explanation:

`D = d^2 = b^2 - 4ac = 1 + 8 = 9` --> `d = +- 3`
This means there are 2 real roots (2 x-intercepts)
`x = -b /(2a) +- d/(2a).`
`x = -1/4 +- 3/4` --> x = -1 and `x = 1/2`

Answer 2

The discriminant is `9`.

A positive discriminant means that there are two real roots (x-intercepts).

Also, since the discriminant is a perfect square, the two roots are rational.

Explanation:

`2x^2+x-1=0` is an quadratic equation in the form of `ax^2+bx+c`, where `a=2, b=1, and c=-1`.

The formula for the discriminant, `"D"`, comes from the quadratic formula, `x=(-b+-sqrt(color(red)(b^2-4ac)))/(2a)` .

`"D"=b^2-4ac` =

`"D"=1^2-4(2)(-1)` =

`"D"=1+8` =

`"D"=9`

A positive discriminant means that there are two real roots (x-intercepts).

Since the discriminant is a perfect square, the two roots are also rational.

Resource:
http://www.regentsprep.org/regents/math/algtrig/ate3/discriminant.htm