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Find the real zeros, if any, of the quadratic f(x)=x^(2)+4x+1

User Canufeel
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Final answer:

The real zeros of the quadratic function f(x) = x^2 + 4x + 1 are approximately -2 + sqrt(3) and -2 - sqrt(3).

Step-by-step explanation:

To find the real zeros of the quadratic function f(x) = x^2 + 4x + 1, we can start by factoring the quadratic equation or using the quadratic formula. In this case, we will use the quadratic formula.

The quadratic formula states that for a quadratic equation of the form ax^2 + bx + c = 0, the solutions for x are given by:

x = (-b ± sqrt(b^2 - 4ac)) / (2a)

Substituting the values of a, b, and c from the given function f(x) = x^2 + 4x + 1, we can calculate the real zeros:

x = (-4 ± sqrt(16 - 4(1)(1))) / (2(1))

Simplifying further:

x = (-4 ± sqrt(12)) / (2)

x = (-4 ± sqrt(4*3)) / (2)

x = (-4 ± 2*sqrt(3)) / (2)

x = -2 ± sqrt(3)

Therefore, the real zeros of the quadratic function f(x) = x^2 + 4x + 1 are approximately:

x ≈ -2 + sqrt(3)

x ≈ -2 - sqrt(3)

User Ritesh Bansal
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