Consider the following quadratic equation:
−3y^2−2=−6y
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 use the discriminant, we need to compare the given quadratic equation to the standard form of a quadratic equation: ax^2 + bx + c = 0.
In this case, we have -3y^2 - 6y - 2 = 0.
So, a = -3, b = -6, and c = -2.
The discriminant is given by b^2 - 4ac.
Plugging in the values, we get discriminant = (-6)^2 - 4(-3)(-2) = 36 - 24 = 12.
Since the discriminant is positive, we have two distinct real solutions for the quadratic equation.
Now, we can use the quadratic formula to solve for y:
y = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the values, we get:
y = (-(-6) ± √(36 - 4*(-3)*(-2))) / (2*(-3))
= (6 ± √(36 - 24)) / (-6)
= (6 ± √12) / (-6)
= (6 ± 2√3) / (-6)
= (-1 ± √3/3)
So, the solutions to the equation -3y^2 - 6y - 2 = 0 are:
y = (-1 + √3/3) and y = (-1 - √3/3)