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vladimir1956 [14]
3 years ago
13

If 1 and -1 are the zeroes of the polynomial p(x) = ax 3 + x 2 − 2x + b, find the values of a and b

Mathematics
1 answer:
vampirchik [111]3 years ago
6 0

Answer:

<h2>              a = 2,    b = -1  </h2>

Step-by-step explanation:

p(x) = ax³ + x² - 2x + b

p(1) = a(1)³ + 1² - 2•1 + b = a + 1 - 2 + b = a + b - 1

a + b - 1 = 0  ⇒   b = 1 - a

p(-1) = a(-1)³ + (-1)² - 2(-1) + b = -a + 1 + 2 + b = - a + b + 3

- a + b + 3 = 0    ∧   b = 1 - a

- a + (1 - a) + 3 = 0

- a + 1 - a + 3 = 0

-2a + 4 = 0

-2a = -4

 <u>a = 2</u>

<u>b = 1 - 2 = -1</u>

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