Question

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 1

Answer:

• 3 and 15 are the values of a and b respectively.

Step-by-step explanation:

Given,

• p(x) = x³ - ax² - 13x + b.
• Factors: (x - 1) & (x + 3).

So,

• x = 1 & -3 are the roots of p(x).

Place x as 1:

⇒ (1)³ -a(1)² -13(1) + b = 0

⇒ 1 - a - 13 + b = 0

⇒ -a + b = 12 - (1)

Place x as -3:

⇒ (-3)³ -a(-3)² -13(-3) + b = 0

⇒ -27 - 9a + 39 + b = 0

⇒ -9a + b = -12 - (2)

Subtract (1) from (2):

⇒ -a + b = 12

⇒ -9a + b = -12

• 8a = 24
• a = 3

Place a in (1):

⇒ -a + b = 12

⇒ -3 + b = 12

• b = 15

∴ The values of a and b are 3 and 15.

Answer 2

Answer:

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Step-by-step explanation:

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