Question

Find all the zeroes of polynomial x3+3x2_5x_15 if two of its zeroes are root5 _root5

Answer 1

Hey mate

Here is your solution

Since √5 and -√5 are the two zeroes .

                  x = √5

               ⇒ (x - √5) = 0

       and,

                 x = -√5

            ⇒ (x +√5) = 0

∴ ( x - √5 )( x + √5 ) is a factor of the given polynomial .

We have ,

          ( x - √5 ) ( x +√5 )

        = x² - 5

Now , x³ + 3x² - 5x - 15 ÷ x² - 5 and the quotient we get is x + 3 .

      ∴ So the other zero is x = -3 .

Hope it helps

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