Question
(x2 – 1) is a factor of f(x) = (x5 + ax4 + bx3 + cx2 + x + d). The graph of f(x) intersects the Y axis at (0, –3). Find the value of (a + c).
Answer: Option E
:
E
(x2 -1) = (x – 1) (x + 1) is a factor of f(x).
So, f(1) = f(-1) = 0
1 + a + b + c + 1 + d = –1 + a + b + c – 1 + d
b = -2
(1 + a + b + c + 1 + d) = 0
(–1 + a + b + c – 1 + d) = 0
i.e., a + b + c + d = 2
a – b + c + d = 2.
Since graph passes through (0, –3)
f(0) = –3 or d = –3
∴a + b + c = 1 and a – b + c = 5
∴a + c = 3 Hence option (e)
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:
E
(x2 -1) = (x – 1) (x + 1) is a factor of f(x).
So, f(1) = f(-1) = 0
1 + a + b + c + 1 + d = –1 + a + b + c – 1 + d
b = -2
(1 + a + b + c + 1 + d) = 0
(–1 + a + b + c – 1 + d) = 0
i.e., a + b + c + d = 2
a – b + c + d = 2.
Since graph passes through (0, –3)
f(0) = –3 or d = –3
∴a + b + c = 1 and a – b + c = 5
∴a + c = 3 Hence option (e)
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