Question

if -1 and 2 are the zeroes of the polynomial 2x^3-x^2-5x-2 find its third zeroes.


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Answer 1

Step-by-step explanation:

Given: p(x) = 2x³ - x²  - 5x - 2

Since two zeroes are -1 and 2.

⇒ (x + 1)(x - 2)

⇒  x² - x - 2 is also a factor.

Now by dividing the given polynomial by (x² - x - 2)

We can find out the factors.

Long Division method:

x² - x - 2) 2x³ - x² - 5x - 2 (2x + 1

              2x³ - 2x² - 4x

              ------------------------

                           x² - x - 2

                           x² - x - 2

               -----------------------

∴ 2x³ - x² - 5x - 2 = (x² - x - 2)(2x + 1)

Now,

(x² - x - 2)(2x + 1) = 0

⇒ x = -1,2,-1/2

Hence, zeroes of the given polynomial are: -1,2,-1/2

Hope it helps!

Answer 2

2x³ - x² - 5x - 2 = (x² - x - 2)(2x + 1)

Now,

(x² - x - 2)(2x + 1) = 0

⇒ x = -1,2,-1/2

Hence, zeroes of the given polynomial are: -1,2,-1/2