A linear system can have infinite solutions if both systems represent the same line. if a linear system down not represent the same line then it can only have one or no solutions. No solution is if the system is representing parallel lines and one solution represents an intersection of the two lines. in a nonlinear system you can have infinite or up to a maximum of intersections as the highest degree of the systems.
First of all to transfer <span>(2x - 1)(x + 6) = 0 into a form where we can plug it into the quadratic formula we need to use the FOIL method.
</span><span>(2x - 1)(x + 6) = 0
</span> becomes
2x*x+2x*6+-1*x+-1*6
which simplifies to
2x^2 + 12x - x - 6
and then we add like terms to get
2x^2 + 11x - <span>6
</span>
now that it is in the correct form we can identify "a" "b" and "c" by following this form
ax^2 + bx + c
looking back at the equation we got earlier
2x^2 + 11x - <span>6</span>
a=2,b=11,and c=-6




Multiply the numbers.
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Combine multiplied terms into a single fraction.
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Subtract 8 from both sides of the equation.


Multiply all terms by the same value to eliminate fraction denominators.

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Cancel multiplied terms that are in the denominator.
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Multiply the numbers.
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Divide both sides of the equation by the same term.


Simplify.

Solution.
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ノシ

Answer:
yes
Step-by-step explanation:
Answer:

Step-by-step explanation:
<u>Quadratic Function</u>
The quadratic function can be expressed in the following form:

Where a is a real number different from 0, and x1, x2 are the roots or zeroes of the function.
From the conditions stated in the problem, we know
x_1=1+\sqrt{2}, \ x_1=1-\sqrt{2}
Substitute in the general formula above:
![y=a[x-(1+\sqrt{2})][x-(1-\sqrt{2})]](https://tex.z-dn.net/?f=y%3Da%5Bx-%281%2B%5Csqrt%7B2%7D%29%5D%5Bx-%281-%5Csqrt%7B2%7D%29%5D)
Operate the indicated product

To find the value of a, we use the y-intercept which is the value of y when x=0, thus

It follows that

Thus, the required quadratic function is

Or, equivalently
