I have to find the zeros of f(x) = x^2 + 2x-5
can someone start me off so I have an example to work from for the rest of my problems-thank you for your help
The zeros of a function are the values of x which make f(x) equal to zero, or ...
you are looking for the x-intercepts.
so let x^2 + 2x - 5 - 0
Since it does not factor, we have to use the quadratic formula
x = (-2 ± √(4 -4(1)(-5)) )/2
= (-2 ± √24)/2
= (-2 ± 2√6)/2
= -1 ± √6
Thank you so much for showing me-now I can use this as an example
To find the zeros of a quadratic equation like f(x) = x^2 + 2x - 5, we can use the quadratic formula. The quadratic formula states that for any quadratic equation in the form ax^2 + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 1, b = 2, and c = -5. Substituting these values into the quadratic formula, we have:
x = (-(2) ± √((2)^2 - 4(1)(-5))) / (2(1))
Simplifying further:
x = (-2 ± √(4 + 20)) / 2
x = (-2 ± √(24)) / 2
x = (-2 ± 2√(6)) / 2
Now we can simplify the expression:
x = -1 ± √(6)
So the zeros of f(x) = x^2 + 2x - 5 are x = -1 + √(6) and x = -1 - √(6).
Certainly! To find the zeros of a function, you are essentially looking for the values of x for which the function equals zero. In other words, you need to solve the equation f(x) = 0.
In this case, you have the function f(x) = x^2 + 2x - 5. To find the zeros, set f(x) equal to zero and solve for x:
x^2 + 2x - 5 = 0
To solve this quadratic equation, you can use various methods, such as factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula in this example.
The quadratic formula states that for an equation in the form of ax^2 + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our equation, a = 1, b = 2, and c = -5. Substituting these values into the formula:
x = (-(2) ± √((2)^2 - 4(1)(-5))) / (2(1))
Simplifying:
x = (-2 ± √(4 + 20)) / 2
x = (-2 ± √24) / 2
Now, let's simplify the square root:
x = (-2 ± 2√6) / 2
Next, cancel out the common factors:
x = -1 ± √6
So, the zeros of the function f(x) = x^2 + 2x - 5 are x = -1 + √6 and x = -1 - √6.
Remember to always check your answers by substituting them back into the original equation to ensure they satisfy the equation f(x) = 0.