Question

Determine the given value of x is a zero of the given polynomial or not 6x²-x-2 ; x= -½, x = ⅔​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

(-1/2) and 2/3 are zeroes of P(x) .

Step-by-step explanation:

Given,

Polynomial, P(x)

$Polynomial, P(x) = 6 {x}^{2} - x - 2$

Now, we have to check whether x = (-1/2) and x =2/3 are zeroes of P(x)

Let α , β are zeroes of P(x) then P(α) = 0 and P(β) = 0

Now, P(-1/2) =

$Now, \\ P(-1/2) =6 {(-1/2)}^{2} - (-1/2) - 2 \: \\ = 6 \times 1/4 +1/2 - 2 = 3/2 + 1/2 - 2 \\ = 2 - 2 = 0$

P(2/3)

$P(2/3) = 6 {(2/3)}^{2} - 2/3 - 2 \\ = 6 \times 4/9 - 2/3 - 2 \\ = 8/3 - (2/3 + 2) = 8/3 - 8/3 = 0$

Since P(-1/2)= 0 and P(2/3)=0 so, (-1/2) and 2/3 are zeroes of P(x) .