Check whether –2 and 2 are the zeroes of the polynomial x4–16. Check whether 3 and -2 are the zeroes of the polynomial p(x) when p(x) = x square-x-6.
Answers
Step-by-step explanation:
Given :-
1)x⁴-16
2) x²-x-6
To find:-
Check whether –2 and 2 are the zeroes of the polynomial x⁴–16.
Check whether 3 and -2 are the zeroes of the polynomial p(x) when p(x) = x²-x-6.
Solution:-
1)
Given bi-quadratic polynomial P(x) = x⁴-16
We know that
If -2 is a zero of P(x) then by factor theorem P(-2) = 0
=> P(-2) = (-2)⁴-16
=> P(-2) = 16-16
=> P(-2) = 0
Therefore, -2 is a zero of P(x).
We know that
If 2 is a zero of P(x) then by factor theorem P(2) = 0
=> P(2) = (2)⁴-16
=> P(2) = 16-16
=> P(2) = 0
Therefore, 2 is a zero of P(x).
2)
Given quadratic polynomial P(x) =x²-x-6
We know that
If 3 is a zero of P(x) then by factor theorem P(3) = 0
=> P(3) = 3²-3-6
=> P(3) = 9-9
=> P(3) = 0
Therefore, 3 is a zero of P(x).
We know that
If -2 is a zero of P(x) then by factor theorem P(-2) = 0
=> P(-2) = (-2)²-(-2)-6
=> P(-2) =4+2-6
=> P(-2) = 6-6
=> P(-2) = 0
Therefore, -2 is a zero of P(x).
Answer:-
1) -2 and 2 are the zeroes of x⁴-16
2) 3 and -2 are the zeroes of x²-x-6
Used formulae:-
Factor Theorem:-
Let P(x) be a polynomial of the degree greater than or equal to 1 and x-a is another linear polynomial if x-a is a factor of P (x) then P(a) = 0 vice-versa.