CBSE Class 9 Answered
If
x3 + ax2 + bx + 6 has x - 2 as a factor and leaves a
remainder 3 when divided by x - 3, find the values of a and b.
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
Expert Answer
f(x) = x3 + ax2 + bx + 6
Since (x - 2) is a factor therefore
f(2)
= 8 + 4a + 2b + 6 = 0 
2a + b = -7
...(i)
Again, On dividing by (x - 3) it gives remainder 3 therefore
f(3)
= 27 + 9a + 3b + 6 = 3 3a + b = -30
... (ii)
Subtracting (i) from (ii), we get
a = -23
From (i), b = -7 + 46 = 39
Hence, a = -23, b = 39.
Answered by | 04 Jun, 2014, 03:23: PM
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