Question

verify whether 5/2 is zeroes of the polynomial
p(x)=3x power 4-x power 2-5x+1
1.yes it is
2.no it is
3.cannot say
4.none
with explaintion
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Answer 1

QUESTION :

verify whether 5/2 is zeroes of the polynomial

p(x)=3x⁴-x²-5x+1

1.yes it is

2.no it is

3.cannot say

4.none

_____________________

To verify whether 5/2 is zeroes of the polynomial

p(x)=3x⁴-x²-5x+1 we will put x = 5/2 in 3x⁴-x²-5x+1 ( we will find out p(5/2) . If get p(5/2) = 0 then 5/2 is zeroes of the given polynomial . If we don't get p(5/2) = 0 then 5/2 is not the zeroes of the given polynomial.

$p( x ) = 3 {x}^{4} - {x}^{2} - 5x + 1$

Now first put x = 5/2 in p(x)=3x⁴-x²-5x+1.

$p(\dfrac{5}{2} )= 3 {(\dfrac{5}{2} )}^{4} - {(\dfrac{5}{2} )}^{2} - 5(\dfrac{5}{2} ) + 1$

$p(\dfrac{5}{2} )= \dfrac{{1875}}{16} - {(\dfrac{25}{4} )} - (\dfrac{25}{2} ) + 1$

LCM = 16

$p(\dfrac{5}{2} )= \dfrac{{1875 - 100 - 200 + 16}}{16}$

$p(\dfrac{5}{2} )= \dfrac{1591}{16}$

therefore p(5/2) ≠ 0 so 5/2 is not the zeroes of the given polynomial p(x)=3x⁴-x²-5x+1 .

Answer :

Option (2) is correct.