The x-intercepts of the quadratic equation x^2 + 4x = -1 are x = -2 + √3 and x = -2 - √3.
The quadratic equation is x^2 + 4x = -1. To find the x-intercepts, we set the equation equal to zero:
x^2 + 4x + 1 = 0
Now, applying the quadratic formula where a = 1, b = 4, and c = 1, the formula is:
x = (-b ± √(b^2 - 4ac)) / (2a)
Substitute the values:
x = (-4 ± √(4^2 - 4(1)(1))) / (2(1))
Now, calculate the discriminant (b^2 - 4ac):
b^2 - 4ac = 4^2 - 4(1)(1) = 16 - 4 = 12
Now, substitute the discriminant back into the formula:
x = (-4 ± √12) / 2
The square root of 12 can be simplified as 2√3:
x = (-4 ± 2√3) / 2
Simplify the expression:
x = -2 ± √3
So, the two x-intercepts are x = -2 + √3 and x = -2 - √3.
The question probable may be:
Given the equation X^2+4x=-1 , find x intercepts.