Question

Check whether zeroes of the polynomial

Answer 1

p(x)= 3x²-11x+6

p(2/3) = 3(2/3)² -11(2/3) +6

= 4/3-22/3 +6

= -18/3 +6

= -6+6

=0

p(2/3) =0

p(3) = 3(3)²-11(3)+6

= 27 -33 +6

=33-33

=0

p(3)=0

therefore 2/3 ,3 are zeroes of p(x)

Answer 2

Answer:

Yes, both $\rm{\dfrac{2}{3}}$ and $\rm{3}$ are zeros of the

polynomial $\rm{3x^2 - 11x + 6}$.

Step-by-step explanation:

★ As we know, to check whether the 2/3 and 3 are zeroes of the polynomial, we have to put them one by one at the place of x in the given polynomial. If the answer will be zero, then it is confirmed that the 2/3 and 3 are zeros of the given polynomial.

Solution:

$\leadsto\rm{p(x) = 3x^2 - 11x + 6}$

$\rightarrow$ Put x = 2/3

$\rightarrow\rm{p(\dfrac{2}{3}) = 3(\dfrac{2}{3}) - 11(\dfrac{2}{3}) + 6}$

$\rightarrow\rm{p(\dfrac{2}{3}) = \dfrac{4}{3} - \dfrac{22}{3} + 6}$

$\rightarrow\rm{p(\dfrac{2}{3}) = \cancel{\dfrac{-18}{3}} + 6}$

$\rightarrow\rm{p(\dfrac{2}{3}) = \cancel{-} 6 \cancel{+} 6}$

$\rightarrow\fbox{\rm p(\dfrac{2}{3}) = 0}$

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$\leadsto\rm{p(x) = 3x^2 - 11x + 6}$

$\rightarrow$ Put x = 3

$\rightarrow\rm{p(3) = 3(3)^2 - 11(3) + 6}$

$\rightarrow\rm{p(3) = 27 - 33 + 6}$

$\rightarrow\fbox{\rm p(3) = 0}$

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