Question

Find the value of a and b so that the polynomial x^3 - ax^2 - 13x + b has (x-1) and (x+3) as factors . With steps

Answer 1

Since,
(x-1) and (x+3) are factors of polynomial f(x)=
${x}^{3} - a {x}^{2} - 13x + b = 0$
Therefore,
f(1) = 0
=> 1-a-13+b= 0
=> b-a= 12 -----(1)

f(3) = 0
=> 3^3-a3^2-13*3+b=0
=> 27-9a-39+b=0
=> b-9a= 12--------(2)

Solving (1) and (2),
a= 0 b= 12

Answer 2

Answer:

a=0, b=12

Step by Step Explanation:

Since,

(x-1) and (x+3) are factors of polynomial f(x)=

Therefore,

f(1) = 0

=> 1-a-13+b= 0

=> b-a= 12 -----(1)

f(3) = 0

=> 3^3-a3^2-13*3+b=0

=> 27-9a-39+b=0

=> b-9a= 12--------(2)

Solving (1) and (2),

a= 0 b= 12

#Hope it helped

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