How do you find the value of the discriminant and determine the nature of the roots $5b^2+b-2=0$ ?

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Answer 1 · 2017-06-01T19:19:08

The discriminant is $41$ and therefore there are 2 distinct real-number solutions.

If a quadratic equation is in the form:

$ax^2+bx+c$

The discriminant is defined to be:

$b^2-4ac$

$1^2-4(5)(-2)$

$1+40=41$

Since the discriminant is positive, there are 2 distinct real-number solutions.

If the discriminant is negative, there are no real-number solutions and if the discriminant is $0$ , one repeated real-number solution.

How do you find the value of the discriminant and determine the nature of the roots 5b^2+b-2=05b^2+b-2=0?