if p(x)=x^4+ax^3+bx^2+cx+d, p(1)=p(2)=p(3)=0 then find the value of p(4)+p(0)
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p(x) = x⁴ + a x³+b x² + c x + d
If p(1) = p(2) = p(3) = 0, it means that (x-1) , (x-2) , (x-3) are factors of P(x). Let the last factor of P(x) be (x - m). Hence
p(x) = x⁴ + a x³+b x² + c x + d = (x-1) (x - 2 ) ( x - 3 ) (x - m)
comparing the constant term = d = 6m => m = d/6
p(4) + p(0) = 3 * 2 * 1 * (4 - m) + (-1 * -2 * -3 * -m)
= 24 - 6 m + 6m = 24
Answer is 24
If p(1) = p(2) = p(3) = 0, it means that (x-1) , (x-2) , (x-3) are factors of P(x). Let the last factor of P(x) be (x - m). Hence
p(x) = x⁴ + a x³+b x² + c x + d = (x-1) (x - 2 ) ( x - 3 ) (x - m)
comparing the constant term = d = 6m => m = d/6
p(4) + p(0) = 3 * 2 * 1 * (4 - m) + (-1 * -2 * -3 * -m)
= 24 - 6 m + 6m = 24
Answer is 24
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Answer:
answer is 24
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