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How many roots do the functions have in common f(x)=x^2+x-6

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To find the common roots between two functions, we need to find the roots (or solutions) of each function individually and then identify the shared solutions.

For the function f(x) = x^2 + x - 6, we can find the roots by setting the function equal to zero and solving for x:

x^2 + x - 6 = 0

To factorize this quadratic equation, we need to find two numbers that multiply to -6 and add up to 1 (the coefficient of x). The numbers that satisfy these conditions are 3 and -2:

(x + 3)(x - 2) = 0

Setting each factor equal to zero:

x + 3 = 0 or x - 2 = 0

Solving for x in each equation:

x = -3 or x = 2

Therefore, the function f(x) = x^2 + x - 6 has two roots: x = -3 and x = 2.

To find the common roots between this function and another function, we would need to know the second function. If you provide the second function, I can help determine if there are any shared roots.

User Wrufesh
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