Question

evaluate the discriminate and describe the nature of the roots for the equation

Answer 1

??

Answer 2

x^2+8x-10=0

Answer 3

8^2 - 4*1*(-10) = 64 + 40 = 104
- a positive value means there are two unique real roots

Answer 4

real and rational or real and irrational?

Answer 5

they could be rational or irrational

Answer 6

The equation of the discriminant is: \( D = b^2 - 4ac \). Considering the discriminant within the quadratic formula:
\[ x = \frac{-b \pm \sqrt{\color{green}D}}{2a} \]
If \(D\) is positive, we have two cases:
* If \(D\) is a perfect square, then \(\sqrt{D}\) is a positive integer, and we will have two rational solutions.
* If \(D\) is not a perfect square, then \(\sqrt{D}\) is irrational, and we will have two irrational roots.

If \(D\) is zero, then we have a single case: one rational root.

If \(D\) is negative, then \(\sqrt{D}\) is not a real number, and we'll have two complex roots (no real roots).

Answer 7

Thanks

Answer 8

yes - sorry - in the above case the roots are real and irrational

Answer 9

You're welcome! :)