Which is the zero of the polynomial xcube +2x square - 5x-6 a) - 2 B) 2 c) - 3 d) 3
Answers
Given :-
Cubic polynomial
p ( x ) = x³ + 2x² - 5x - 6
Required to find :-
- Zero of the polynomial
Concept used :-
- Hit trial and error method !
Solution :-
Given :-
Cubic expression ;
p ( x ) = x³ + 2x² - 5x - 6
So,
Let's consider that ;
- 2 is the zero of the polynomial
Substitute this value in place of x in p ( x )
So,
p ( - 2 ) =
( - 2 )³ + 2 ( - 2 )² - 5 ( - 2 ) - 6 = 0
- 8 + 2 ( 4 ) + 10 - 6 = 0
- 8 + 8 + 10 - 6 = 0
18 - 14 = 0
=> 4 ≠ 0
Hence,
LHS ≠ RHS
So,
- 2 is not the zero of p ( x )
Similarly,
Let's consider that ;
2 is the zero of the polynomial
Substitute the value of x in p ( x )
So,
p ( 2 ) =
( 2 )³ + 2 ( 2 )² - 5 ( 2 ) - 6 = 0
8 + 2 ( 4 ) - 10 - 6 = 0
8 + 8 - 10 - 6 = 0
16 - 16 = 0
=> 0 = 0
Hence,
LHS = RHS
So,
2 is the zero of polynomial .
However,
Let's verify the other two given values also ;
So,
Let's consider that ;
- 3 is the zero of the polynomial
Substitute this value in place of x in p ( x )
So,
p ( - 3 ) =
( - 3 )³ + 2 ( - 3 )² - 5 ( - 3 ) - 6 = 0
- 27 + 2 ( 9 ) + 15 - 6 = 0
- 27 + 18 + 15 - 6 = 0
33 - 33 = 0
=> 0 = 0
So,
LHS = RHS
Hence,
- 3 is the zero of the polynomial
Similarly ,
Let's consider that ;
3 is the zero of the polynomial
Substitute this value in place of x in p ( x )
So,
p ( 3 ) =
( 3 )³ + 2 ( 3 )² - 5 ( 3 ) - 6 = 0
27 + 2 ( 9 ) - 15 - 6 = 0
27 + 18 - 15 - 6 = 0
45 - 21 = 0
24 ≠ 0
Hence,
LHS ≠ RHS
So,
3 is not the zero of p ( x )
Conclusion :-
From the above results we can conclude that ;
2 & - 3 are the zeroes of the given cubic polynomial
So,