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Question 14
If (x + 1) is a factor of f(x) = 2x3+ax2+2bx+1, then find the value of a and b is given that 2a – 3b = 4.

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Solution

Given that, (x + 1) is a factor f(x) = 2x5+ax2+2bx+1 then f(-1) = 0
[if (x + α) is a factor of f(x) = ax2 + bx + c, then f(-) = 0]
2(1)3+a(1)2+2b(1)+1=0
-2 + a – 2b + 1 = 0
a – 2b – 1 = 0
2a – 3b = 4
3b = 2a – 4
b=(2a43)
Now, put the value of b in Eq. (i), we get
a2(2a43)1=0
3a – 2(2a – 4) – 3 = 0
3a – 4a + 8 – 3 = 0
- a + 5 = 0
a = 5
Now, put the value of b in Eq. (i), we get
a22a431=0
3a – 2(2a – 4) – 3 = 0
- a + 5 = 0
a = 5
Now, put the value of a in Eq (i), we get
5 – 2b – 1 = 0
2b = 4
b = 2
Hence, the required values of a and b are 5 and 2, respectively

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