(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).

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Solution

The correct option is E 3
(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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(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).

(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).