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If p(x) = x ^3 − 3x^ 2 + 2x + 5 and p(a) = p(b) = p(c) = 0, then the value of (2 − a)(2 − b)(2 − c) is

User Buser
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1 Answer

4 votes

Answer: 5

Explanation:

p(x) = x³ - 3x² + 2x + 5 p(a) = p(b) = p(c) = 0

0 = x³ - 3x² + 2x + 5

0 = (x - a)(x - b)(x - c)

= x³ − (a + b + c)x² + (ab + bc + ca)x - abc

↓ ↓ ↓

-3 2 5

-(a + b + c) = -3

a + b + c = 3

ab + bc + ca = 2

-(abc) = 5

abc = -5

(2 - a) (2 - b) (2 - c)

= 8 - 4(a + b + c) + 2(ab + bc + ca) - abc

= 8 - 4(3) + 2(2) -(-5)

= 8 - 12 + 4 + 5

= 5

User Justincely
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