Question

Use the discriminant to describe the roots of each equation. Then select the best description.
x2 - 5x - 4 = 0
double root
real and rational roots
real and irrational roots non-real roots

Answer 1

Answer:

Third option: Real and Irrational roots.

Step-by-step explanation:

For a Quadratic equation:

$ax^2+bx+c=0$

The Discriminant can be found with this formula:

$D=b^2-4ac$

Given the following Quadratic equation:

$x^2 - 5x - 4 = 0$

You can identify that:

$a=1\\b=-5\\c=-4$

Then, substituting these values into the formula for find the Discriminant, you get that this is:

$D=(-5)^2-(4)(1)(-4)\\\\D=41$

Therefore, since the Discriminant is positive ($D>0$) but it is not a perfect square, then the roots of the equation are Real and Irrational.