How many solutions do `6x^2 - 1x + 10 = 0` have? And what type of numbers are they?

Expert Answers

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The discriminant of a quadratic equation in a form `ax^2+bx+c=0` can be used to predict  the number of solutions and its type if it is rational, irrational or a complex number.

The formula is:

`Discriminant = b^2 - 4ac`

If the discriminant is positive and a perfect square, there are two rational solutions.

If it is positive and not a perfect square , there are two irrational solutions.

If the discriminant is equal to zero, there is only one real solution.

And if it is negative, there are two non-real (complex) solutions.

So the discriminant of `6x^2-1x+10=0` is:

`Discriminant = (-1)^2- 4*6*10=1-240=-239`

Hence, there are two non-real solutions. (Or the solutions are two complex numbers.)

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