How do you find the value of the discriminant and determine the nature of the roots $2x^2+3x+1=0$ ?

Question

1495 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-10-03T22:11:45

The Roots are Real, distinct and Rational...

So, go ahead and solve the equation, you will 2 exact answers for the roots!

The discriminant ( $Delta$ ) tells us something about the roots (solutions) of a quadratic equation without us having to solve the equation first.

$Delta = b^2-4ac" where " ax^2 +bx+c=0$

From $" " 2x^2+3x+1=0$

$Delta = 3^2 -4(2)(1) = 9-8 =1$

$Delta =1$

What does this tell us?

If $Delta <0 " "rarr$ the roots are non-real (imaginary)

If $Delta>= 0 " "rarr$ the roots are Real. (they do exist!)

If $Delta = 0 " "rarr$ there are 2 equal roots (ie one answer)

If $Delta > 0 " "rarr$ there are 2 distinct Real roots. (different)

If $Delta "is a square "rarr$ the roots are Rational.

If $Delta "is not a square "rarr$ the roots are Irrational.

$1$ is a perfect square, so the Roots are Real, distinct and Rational.

How do you find the value of the discriminant and determine the nature of the roots 2x^2+3x+1=0 2x^2+3x+1=0?