Determine the value of the discriminant and then state the nature of the roots.
x^2-8x-9=0
root 28 is the discriminant
2 different roots is the nature of the roots
Is that correct?
Thanks a ton! :)
64 - 4*-9 = 100
the discriminant is what is under the square root sign, b^2-4ac
yes, roots are 9 and -1
The Discriminant is greater than zero(100); therefore, we have 2 real roots.
To determine the value of the discriminant, you can use the formula Δ = b^2 - 4ac, where a, b, and c are the coefficients of the quadratic equation in the form ax^2 + bx + c = 0.
Here, the equation is x^2 - 8x - 9 = 0, so a = 1, b = -8, and c = -9. Plugging these values into the discriminant formula, we get:
Δ = (-8)^2 - 4(1)(-9)
= 64 + 36
= 100
So, the value of the discriminant is 100.
To state the nature of the roots, we look at the value of the discriminant:
- If Δ > 0, then the equation has two different real roots.
- If Δ = 0, then the equation has one real root (which is a repeated root or a "double root").
- If Δ < 0, then the equation has two complex roots (no real solutions).
In this case, since the value of the discriminant (Δ = 100) is positive, we can conclude that the equation x^2 - 8x - 9 = 0 has two different real roots.
So, you're correct! The value of the discriminant is 100, and the nature of the roots is that they are two different roots.