Question

In the following , determine whether the given values of x are zeroes of the given polynomial or not 6x2 - x - 2 ; x = - 1 / 2 , x = 2 / 3. ​

Answer 1

Given : polynomial  6x² - x - 2

x = - 1/2  

x = 2/3

To Find :  determine whether the given values of x are zeroes of the given polynomial or not

Solution:

6x² - x - 2

=  6x² + 3x - 4x - 2

= 3x(2x + 1) -2(2x + 1)

= (2x + 1)(3x -2)

6x² - x - 2 =  (2x + 1)(3x -2)

Zeroes of polynomial

(2x + 1) = 0  => x = - 1/2

(3x-2) = 0 => x =2/3

Hence x  = - 1/2  and 2/3 are zeroes of   given polynomial  6x² - x - 2

Another method:

p(x) = 6x² - x - 2

p(-1/2) =  6(-1/2)² - (-1/2) -  2= 0

p(2/3) = 6(2/3)²  - 2/3 - 2 =  0

Hence -1/2 and 2/3 are zeroes of  given polynomial  6x² - x - 2

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