(2018)
21. If (x + 2) and (x - 3) are factors of x3 + ax + b, find the values of a and b. With these
values of a and b, factorise the given expression.
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Answer:
Hello Mate!
Polynomial we have is p(x) = x³ + ax + b
Since two of the factors are ( x + 2 ) and ( x - 3 ) so respective value of x = - 2 and 3.
Keeping values if x we get,
p(x) = -2³ + a(-2) + b
0 = - 8 - 2a + b
8 = - 2a + b or - 8 = 2a - b __(1)
p(x) = 3³ + a(3) + b
- 27 = 3a + b __(2)
On adding (1) and (2)
- 35 = 5a
- 7 = a
Keeping value of a in equation (1) we get
- 8 = 2(-7) - b
- 8 + 14 = - b
- 6 = b
So, p(x) = x³ + ax + b
p(x) = x³ + 0x² - 7x - 6
Please refer to attatchment above!
Hence other factor is ( x + 1 ).
So zeros if polynomial are x = - 2, + 3 and - 1.
Have marvelous future ahead!
PLZZ MARK BRAINLIEST........
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