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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

User Alvarado
by
8.2k points

1 Answer

3 votes

Answer:

Third option: Real and Irrational roots.

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.

User Abdallah Arffak
by
8.5k points

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