find the value of A and B such that the polynomial f of x is equal to 3 x cube + x square - 13 x + b is divisible by x square - 2 x minus 3
Answers
⠀⠀⠀⠀ ☛ Solution ☚⠀ ⠀
⠀ ⠀
polynomial , x³ -ax² -13x + b has two factors ( x -1) and (x +3)
it means , x = 1 and -3 are the roots (zeros ) of x³ -ax² -13x + b...
so,
put x = 1 in polynomial ,.
- (1)³ -a(1)² -13(1) + b = 0
- 1 - a -13 + b = 0
- -a + b = 12 ---------(1)
put x = -3
- (-3)³ -a(-3)² -13(-3) + b = 0
- -27 -9a +39 + b = 0
- -9a + b = -12 --------(2)
subtract equation (1) and (2)
- - a + b + 9a - b = 12 + 12
- 8a = 24
- a = 3
put a = 3 in equation (1)
- b = 15
Therefore, the value of a is 3 and value of b is 15...⠀
Answer:
polynomial , x³ -ax² -13x + b has two factors ( x -1) and (x +3)
it means , x = 1 and -3 are the roots (zeros ) of x³ -ax² -13x + b...
so,
put x = 1 in polynomial ,.
(1)³ -a(1)² -13(1) + b = 0
1 - a -13 + b = 0
-a + b = 12 ---------(1)
put x = -3
(-3)³ -a(-3)² -13(-3) + b = 0
-27 -9a +39 + b = 0
-9a + b = -12 --------(2)
subtract equation (1) and (2)
- a + b + 9a - b = 12 + 12
8a = 24
a = 3
put a = 3 in equation (1)
b = 15
Therefore, the value of a is 3 and value of b is 15...
Step-by-step explanation: