What are the roots of g(x)=4x2+256
? Provide the exact answers. Enter the smaller number first.(1 point)
The roots are
and
.
To find the roots of the given quadratic equation g(x) = 4x^2 + 256, we need to set g(x) equal to zero and solve for x.
Setting g(x) equal to zero:
4x^2 + 256 = 0
Now we can solve for x by factoring out a common factor of 4:
4(x^2 + 64) = 0
Next, we apply the zero product property:
4 = 0 or x^2 + 64 = 0
The first equation, 4 = 0, is not possible as it leads to a contradiction. So we disregard it.
Solving the second equation, x^2 + 64 = 0, by subtracting 64 from both sides:
x^2 = -64
Taking the square root of both sides:
x = ±√(-64)
Since we cannot take the square root of a negative number in the real number system, the given quadratic equation has no real roots.
Therefore, there are no exact answers for the roots of g(x) = 4x^2 + 256.