help me with question 14' third part!
R1= 5a-6
R2=4a-10
please help me.. I'm posting it third time!
Answers
I hope this might clear ur doubts.
Answer:
(i) a = (-4)
(ii) a = (16/9)
(iii) a = (11/7)
Step-by-step explanation:
We have,
x³ + 2x² - 5ax - 7 and x³ + ax² - 12x + 6 divided by (x + 1) and (x - 2) respectively.
Now,
Using Remainder theorem,
Let p(x) = x³ + 2x² - 5ax - 7
and g(x) = x + 1
Since,
p(x) is divided by g(x).
x + 1 = 0
x = -1
So,
p(-1) = (-1)³ + 2(-1)²- 5a(-1) - 7
R1 = -1 + 2(1) + 5a - 7
R1 = 5a - 8 + 2
R1 = 5a - 6
Similarly,
Using Remainder theorem,
Let f(y) = x³ + ax² - 12x + 6
g(y) = (x - 2)
So,
x - 2 = 0
x = 2
Then,
f(2) = 2³ + a(2)² - 12(2) + 6
R2 = 8 + 4a - 24 + 6
R2 = 4a - 24 + 14
R2 = 4a - 10
Now, according to the Question,
Case 1
R1 = R2
5a - 6 = 4a - 10
5a - 4a = 6 - 10
a = -4
Case 2
R1 + R2 = 0
(5a - 6) + (4a - 10) = 0
5a - 6 + 4a - 10 = 0
9a - 16 = 0
9a = 16
a = 16/9
Case 3
2R1 + R2 = 0
2(5a - 6) + (4a - 10) = 0
10a - 12 + 4a - 10 = 0
14a - 22 = 0
14a = 22
a = 22/14
a = 11/7
Hope it helped and believing you understood it........All the best