Question 1177172
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                I have another solution and different answer.



<pre>
We are given a polynomial of EVEN degree


    f(x) = a(n)x^n + a(n-1)x^(n-1) + . . . + a(1)x + a(0)


with negative leading coefficient a(n) < 0 and with positive constant term a(0) > 0.



It means that the polynomial f(x) is negative and remains to be negative at x ---> -oo

                        and also  is negative and remains to be negative at x --->  oo.


At the same time, the polynomial f(x) has  positive value at x= 0:  f(0) = a(0) > 0   (given).


Hence, under given/imposed conditions, the polynomial f(x) has at least two zeroes: 

    - at lest one positive root 

and

    - at least one negative root.



<U>ANSWER</U>.  At given conditions, the polynomial f(x) has at least two x-intercepts: 

         at least one positive x-intercept and at least one negative x-intercept.
</pre>


Solved, answered and explained. And completed.


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As a visual model and as a visual check, imagine a quadratic polynomial y = -x^2 + 1.