Use the value of the discriminant to determine the nature of the roots of the quadratic: x2 - 10x + 25 = 0

Answer 1

Hi...

In the quadratic equation, the DISCRIMINANT is the term b² - 4ac. This is the term inside in the √ sign. Remember it is the term inside √ sign, NOT the final √ value

For the given equation x² - 10x + 25 = 0

The value of 'a' is the coefficient with the x² term, which is 1

The value of 'b' is the coefficient with the x term, which is -10, don't forget the sign!

The value of 'c' is the constant, which is 25

Therefore, the DISCRIMINANT is (-10)² - 4(1)(25) = 100 - 100 = 0

Remember...

If the DISCRIMINANT is POSITIVE, the equation has TWO real sol's

If the DISCRIMINANT is ZERO, the equation has only ONE real sol ⇐ This is the nature of the roots

If the DISCRIMINANT is NEGATIVE, the equation has TWO complex so

Hope this helps...

Answer 2

The discriminant is the expression under the radical in the quadratic formula. It is:

b² - 4ac

where a is the coefficient of the x² term, b is the coefficient of the x term, and c is the constant in the quadratic equation. In your case, a = 1, b = -10, and c = 25. Plug those values into the discriminant.

1. If the discriminant is greater than zero, then the quadratic will have two real roots
2. If the discriminant equals 0, then the quadratic will have one real root
3. If the discriminant is less than zero, then the quadratic equation will have two complex roots and no real roots