Question

What is the discrimant of x^2 +x-2=0

Answer 1

Discriminant = 9.

Explanation:

Discriminant

`\boxed{b^2-4ac}\quad\textsf{when}\;ax^2+bx+c=0`

`\textsf{when $b^2-4ac > 0 \implies$ two real roots}.`

`\textsf{when $b^2-4ac=0 \implies$ one real root}.`

`\textsf{when $b^2-4ac < 0 \implies$ no real roots}.`

Given function:

`x^2+x-2=0`

Therefore:

• a = 1
• b = 1
• c = -2

Substitute the values of a, b and c into the discriminant formula:

`\begin{aligned} \implies b^2=4ac&=(1)^2-4(1)(-2)\\&=1-4(-2)\\&=1+8\\&=9\end{aligned}`

Therefore, the discriminant of the given function is 9.

As the discriminant is greater than zero, this implies that there are two real roots.