Find the discriminant for the quadratic equation f(x) = 5x^2 - 2x + 7 and describe the nature of the roots.
discriminant is 144, one real root
discriminant is -136, two complex roots <--?
discriminant is -136, one complex root
discriminant is 144, two real roots
If a binomial, x - a, divides a polynomial, what must be true in order for x - a to be a factor of the polynomial?
The remainder has to be 0.
The polynomial must be degree 3.
It must divide the polynomial in half. <-- ?
There cannot be any other factor x = a.
one out of two
if something goes into something else "evenly" (wholly), then ...
Which one is correct and huh? sorry I'm lost
1st one is correct
the division hint is for the 2nd
Thanks! :)
To find the discriminant of a quadratic equation of the form f(x) = ax^2 + bx + c, you can use the formula Δ = b^2 - 4ac, where Δ represents the discriminant. For the given equation f(x) = 5x^2 - 2x + 7, a = 5, b = -2, and c = 7.
Plugging these values into the discriminant formula, we get Δ = (-2)^2 - 4(5)(7) = 4 - 140 = -136. Therefore, the discriminant for the given equation is -136.
Now, let's analyze the nature of the roots based on the discriminant value:
- If the discriminant is positive (Δ > 0), then the quadratic equation has two distinct real roots. In this case, since the discriminant is -136, which is negative, we can conclude that the equation has two complex roots.
Thus, the correct answer is "discriminant is -136, two complex roots."