ax ^ 2 + bx + c = 0. This is exactly the form the quadratic equation has. The letters a, b, and c can be any real number, but a must never be zero.
Before x ^ 2 there is a coefficient a, which in our equation is equal to:
a = 3.
Before x is the coefficient b, which in our equation is:
b = -15.
Without x, this is the coefficient c, which our equation has:
c = 0.
The discriminant is a number equal to b ^ 2 – 4ac: D = b ^ 2 – 4ac = -15 ^ 2 – 4 * 3 * 0 = 225.
We are always looking for the discriminant to know the number of roots of a quadratic equation. If D <0, then there are no roots. If D = 0, then one root. If D> 0, then there are two roots. In our case:
D> 0, so there will be two roots: x = (-b ± D ^ (1/2)) / (2a).
D ^ (1/2) = 15.
x1 = (15 + 15) / (2 * 3) = 5.
x2 = (15 – 15) / (2 * 3) = 0.
Answer: 5, 0.
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