Use the discriminant to determine whether each quadratic equation has two unequal real solutions, a repeated real solution, or no solution, WITHOUT solving each equation below.
(1) x^2 + 5x + 7 = 0
(2) 2x^2 - 3x + 4 = 0
NOTE: What is the correct definition of a discriminant?
Check the discriminant, as it says. If it's positive, then you have 2 unequal real roots. If it's negative, no real roots. If it's 0, one root of multiplicity 2.
The discriminant is what's under the radical in the quadratic formula.
I simply plug the value of a, b and c as found in each equation into the discriminant, right?
Afterward, I simplify, right?
Originally Posted by symmetry
that's 100% correct.
With your first example:
a = 1
b = 5
c = 7
Thus the discriminant d = 5²-4*1*7=-3. Therefore there exists no real solution.
Boy, this is very easy stuff. The question itself is not clear when first read but none the less very easy to handle.