Question

4. Find all the zeroes of the polynomial 3x4 + 6x3 - 2x2 - 10x - 5, if two of its zeroes are V5/3 and -V5/3
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Answer 1

Answer:

Here is your answer

Step-by-step explanation:

Let's assume √5/3 and -√5/3 are the factors of the polynomial

x + √5/3 = 0 , x - √5/3 = 0

(x+√5/3) (x-√5/3) = 0

x² - (√5/3)² = 0               using (a+b) x (a-b) = a² - b² identity

x² - 5/3 = 0

x² - 5/3√ 3x^4 + 6x³ - 2x² - 10x - 5     quotient = 3x² + 6x + 3

               3x^4 + 0x³ - 5x²

              (-)     (-)      (+)

                         6x³ + 3x² - 10x

                         6x³ - 0x² - 10x

                         (-)    (-)     (+)

                                 3x² + 0x - 5

                                -3x² - 0x + 5

                                  =  0

3x² + 6x + 3 = 0

÷ by 3

 x² + 2x + 1 = 0

 x² + x + x + 1 = 0

 x ( x+1) 1 (x+1) = 0

 x = -1,-1

So the zeroes are  -1,-1,  V5/3 and -V5/3