Consider the following quadratic equation:
−y^2−4y−4=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 quadratic equation -y^2 - 4y - 4 = 0, we need to use the discriminant, which is b^2 - 4ac.
In this equation, a = -1, b = -4, and c = -4. Substituting these values into the formula for the discriminant, we have:
b^2 - 4ac = (-4)^2 - 4(-1)(-4)
= 16 - (-16)
= 16 + 16
= 32
The discriminant is positive (32 > 0), which means that there are two distinct real solutions for the quadratic equation.
Now we can solve the quadratic equation using the formula: y = (-b ± √(b^2 - 4ac)) / (2a)
Substituting the values a = -1, b = -4, and c = -4 into the formula, we have:
y = (4 ± √(4^2 - 4(-1)(-4))) / (2(-1))
= (4 ± √(16 - 16)) / (-2)
= (4 ± √0) / (-2)
Since the discriminant equals 0, the square root term becomes √0 = 0. Therefore, the equation becomes:
y = (4 ± 0) / (-2)
= (4 + 0) / (-2) or (4 - 0) / (-2)
= 4 / (-2) or 4 / (-2)
= -2 or -2
The solutions to the quadratic equation -y^2 - 4y - 4 = 0 are y = -2 and y = -2.