Question

How do you find the discriminant `x^2+x-12`?

Answer 1

49

Explanation:

Given a quadratic equation in standard form `ax^2 +bx+c=0`

Then the discriminant `color(red)(|bar(ul(color(white)(a/a)color(black)((Delta)=b^2-4ac)color(white)(a/a)|)))`

The value of the discriminant gives information on the `color(blue)" nature of the roots "`

`• b^2-4ac > 0 " roots are real and irrational "`

However if `b^2-4ac " is a square , roots are real and rational"`

`• b^2-4ac=0 " roots are real and equal "`

`• b^2-4ac < " roots are not real "`

For the given function here `x^2+x-12 , a=1,b=1,c=-12`

`rArr b^2-4ac=1^2-(4xx1xx-12)=49`

Since `b^2-4ac > 0 " and a square , roots will be real and rational"`