I'm having a problem in this question.
x^{2} +3x-10 is a factor of x^{3} +ax^{2} +bx+30
How do you find a and b?
Answers
Factorising x² - 3x + 2 we get
[Splitting the middle term]
x² - 2x - x + 2 = 0
=> x (x - 2) -1( x - 2) = 0
=> (x - 1)(x - 2) = 0
This means x - 1 and x - 2 are factors of
x³ + ax² - bx + 10
at x - 1 = 0
we get x = 1
Putting the value we get
(1)³ + a(1)² - b(1) + 10 = 0 (since it is a factor)
=> 1 + a - b + 10 = 0
=> a - b = -10 -1
=> a - b = -11.............(i)
Now at x - 2
x - 2 = 0
=> x = 2
Putting the value we get
(2)³ + a(2)² - b(2) + 10 = 0
=> 8 + 4a - 2b + 10 = 0
=> 4a - 2b + 18 = 0
=> 4a - 2b = -18
=> 2(2a - b) = -18
=> 2a - b =-18/2
=> 2a - b = -9.......... (ii)
Subtracting (i) from (ii) we get
2a - b -(a - b) = -9 - (-11)
=> 2a- b - a + b = -9 + 11
=> a = 2
Now putting the value of a in (i)
2 - b = -11
=> -b = -11 - 2
=> -b = -13
=> b = 13
a = 2 and b = 13
Answer:
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