Find the values of a and b so that the polynomial x³ - ax² - 13x + b has x - 1 and X + 3 as factors.
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Answer:
a = 3 and b = 15
Step-by-step explanation:
Given, polynomial is p(x) = x³ - ax² - 13x + b
Given, x - 1 and X + 3 are the factors of p(x)
=> p(1) = 0 and p(-3) = 0
=> 1 - a - 13 + b = 0 and -27 -9a + 39 + b = 0
=> -a + b = 12 -----(1) and 9a - b = 12 ---------(2)
solving (1) & (2), we get
a = 3 and b = 15.
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