Consider the following quadratic equation:
3y^2−1=0
Step 2 of 2 : Use the discriminant, b2−4ac
, to determine the number of solutions of the given quadratic equation. Then solve the quadratic equation using the formula y=−b±b2−4ac⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯/2a
.
To determine the number of solutions of the given quadratic equation using the discriminant, we need to consider the value of the discriminant (b^2 - 4ac).
In the quadratic equation 3y^2 - 1 = 0, we have:
a = 3
b = 0
c = -1
The discriminant is given by: b^2 - 4ac
Substituting the values, we get:
0^2 - 4(3)(-1)
= 0 + 12
= 12
Since the discriminant is positive (12 > 0), there are two real solutions for the quadratic equation.
Now, let's solve the quadratic equation using the formula y = (-b ± √(b^2 - 4ac)) / (2a):
Substituting the values, we get:
y = (-(0) ± √(0^2 - 4(3)(-1))) / (2(3))
y = ± √(12) / 6
y = ± √(4 * 3) / 6
y = ± (2√3) / 6
y = ± √3 / 3
Therefore, the quadratic equation 3y^2 - 1 = 0 has two real solutions, which are y = √3 / 3 and y = -√3 / 3.