Solve the Quadratic Function -2x² - 8x - 10: Find x When f(x) > 0

Question

Look at the following function:

y=−2x2−8x−10 y=-2x^2-8x-10

Determine for which values of x x the following is true:

f\left(x\right)>0

Step-by-Step Solution

To solve for where y=−2x2−8x−10>0 y = -2x^2 - 8x - 10 > 0 , we must analyze the quadratic equation.

First, identify the coefficients: a=−2 a = -2 , b=−8 b = -8 , and c=−10 c = -10 .
The parabola opens downwards since a<0 a < 0 .

Calculate the discriminant Δ=b2−4ac=(−8)2−4(−2)(−10)=64−80=−16 \Delta = b^2 - 4ac = (-8)^2 - 4(-2)(-10) = 64 - 80 = -16 .
Since the discriminant is negative, there are no real roots.

As a result, the quadratic does not intersect the x-axis, meaning it has no intervals where it is positive.
Because the parabola opens downward and lies entirely below the x-axis, the function y=−2x2−8x−10 y = -2x^2 - 8x - 10 has no positive domain.

Thus, the function f(x)=−2x2−8x−10 f(x) = -2x^2 - 8x - 10 is never greater than zero.

Therefore, the solution to the problem is The function has no positive domain.

Answer

The function has no positive domain.

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