Question

verify whether 2 ,3 and 1/2 are the zeros of the polynomial P (x)=2 x cube - 11 X square + 17 x minus 6​

Answer 1

Answer: only 1/2is the zero of polynomial

Step-by-step explanation:

Answer 2

Solution :-

We have to check whether

2 , 3 and 1/2 are the zeros of

p(x) = 2x³ - 11x² + 17x - 6

Now as we know that is any number is a factor of the given Polynomial then by replacing it with x in the equation will result in zero .

i.e if α is the root of polynomial p(x) then p(α) = 0 .

Now by putting the values

Checking for 2 :-

p(2) = 2(2)³ - 11(2)² + 17(2) - 6

p(2) = 2(8) - 11(4) + 17(2) - 6

p(2) = 16 - 44 + 34 - 6

p(2) = 50 - 50

p(2) = 0

So 2 is a factor of p(x)

Checking for 3

p(3) = 2(3)³ - 11(3)² + 17(3) - 6

p(3) = 2(27) - 11(9) + 17(3) - 6

p(3) = 54 - 99 + 51 - 6

p(3) = 105 - 105

p(3) = 0

So 3 is a factor of p(x)

Checking for 1/2

$p\left(\dfrac{1}{2}\right) = 2\left(\dfrac{1}{2}\right)^3 - 11\left(\dfrac{1}{2}\right)^2 + 17\left(\dfrac{1}{2}\right) - 6$

$p\left(\dfrac{1}{2}\right) = 2\left(\dfrac{1}{8}\right) - 11\left(\dfrac{1}{4}\right) + 17\left(\dfrac{1}{2}\right) - 6$

$p\left(\dfrac{1}{2}\right) = \dfrac{1}{4} - \dfrac{11}{4} + \dfrac{17}{2} - 6$

$p\left(\dfrac{1}{2}\right) = \dfrac{1 - 11+ 34 - 24}{4}$

$p\left(\dfrac{1}{2}\right) = \dfrac{35 - 35}{4}$

$p\left(\dfrac{1}{2}\right) = \dfrac{0}{4}$

So p(1/2) is factor of p(x)