If f(x)=x-6 and g(x)=x^1/2(x+3) , find g(x) x f(x). A. B. C. D.
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Answer:
The graph crosses the x-axis 2 times
The solutions are x = -8 & x = 4
Step-by-step explanation:
Qaudratics are in the form
Where a, b, c are constants
Now, let's arrange this equation in this form:
Where
a = 1
b = 4
c = -32
We need to know the discriminant to know nature of roots. The discriminant is:
If
- D = 0 , we have 2 similar root and there is 2 solutions and that touches the x-axis
- D > 0, we have 2 distinct roots/solutions and both cut the x-axis
- D < 0, we have imaginary roots and it never cuts the x-axis
Let's find value of Discriminant:
Certainly D > 0, so there are 2 distinct roots and cuts the x-axis twice.
We get the roots/solutions by factoring:
Thus,
The graph crosses the x-axis 2 times
The solutions are x = -8 & x = 4