SOLUTION: Find all real zeros of the function y=x^3 - 2 x^2

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Question 977664: Find all real zeros of the function y=x^3 - 2 x^2 - 25 x +50.
Answer by ikleyn(52787)   (Show Source):
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Solution 1

The polynomial = has the real root = .
Indeed, it is easy to check: = .

Hence, this polynomial can be factored

= .

with he linear factor , where    is a quadratic polynomial.

To find , divide the polynomial    by (long division).
If you perform this division, you will get

= ..

Hence, two other roots of the given polynomial are the roots of the quadratic polynomial , i.e. = and = .

Answer. The roots of the given polynomial    are 2, 5 and -5.

Solution 2

You can get factoring the polynomial    by grouping its terms:

= - = - = .

It gives you the same roots.

SOLUTION: Find all real zeros of the function y=x^3 - 2 x^2 - 25 x +50.