Let P(x) = 3x³-ax+b. If P(1) = P(-1) and P(2)=16, find the values of a and b
1 answer:
P(1) = P(-1) P(1) = 3 - a + b P(-1) = -3 + a + b -> 3 - a + b = -3 + a + b -> 3 - a + b + 3 - a - b = 0 -> 6 - 2a = 0 -> a = 3. P(2) = 24 - 2a + b -> 24 - (2a - b) = 16 -> 2a - b = 8 -> 6 - b = 8 b = -2. So, a = 3 and b = -2 Recheck : P(1) = 3 - 3 + (-2) = -2 P(-1) = -3 + 3 + (-2) = -2 => P(1) = P(-1) (true) P(2) = 24 - 6 + (-2) = 16.
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