Find the range of values of 'c' for which g(x)= -3x^2-4x-c has complex roots
complex roots means negative discriminant. so,
(-4)^2 - 4(-3)(-c) < 0
16-12c < 0
c < 4/3
To find the range of values of 'c' for which the quadratic equation g(x) = -3x^2 - 4x - c has complex roots, we need to determine the discriminant of the equation.
The discriminant of a quadratic equation in the form ax^2 + bx + c = 0 is given by the formula: Δ = b^2 - 4ac.
For the given equation g(x) = -3x^2 - 4x - c, the values of a, b, and c are:
a = -3
b = -4
c = -c (rewrite it as -c to match the format ax^2 + bx + c)
Now, let's calculate the discriminant:
Δ = (-4)^2 - 4(-3)(-c)
= 16 - 12c
= 12 - 12c
For complex roots, the discriminant Δ < 0. So:
12 - 12c < 0
Solving this inequality for 'c', we can isolate 'c' on one side:
12c > 12
Now, dividing both sides by 12, we get:
c > 1
Therefore, the range of values of 'c' for which the quadratic equation g(x) = -3x^2 - 4x - c has complex roots is c > 1.