find the value of a, if (x-a) is a factor of x^3-ax^2+2x+2
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Answered by
1
Answer:
Answer
⇒ (x−a) is factor of x
3
−ax
2
+2x+a−1
⇒ Then, a is the zero of polynomial p(x)=x
3
−ax
2
+2x+a−1
⇒ p(x)=x
3
−ax
2
+2x+a−1
⇒ p(a)=(a)
3
−a(a)
2
+2(a)+a−1
⇒ 0=a
3
−a
3
+2a+a−1
⇒ a
3
−a
3
+2a+a−1=0
⇒ 3a−1=0
⇒ 3a=1
∴ a=
3
1
Answered by
0
Answer
a = -2
Step-by-step explanation
x - a is factor of polynomial ⇒ x - a = 0 ⇒ x = a
Given Polynomial : p(x) = x³ - ax² + x + 2
- Substitute x = a in polynomial p(x)
x³ - ax² + x + 2 = 0
⇒ a³ - a(a)² + a + 2 = 0
⇒ a³ - a³ + a + 2 = 0
⇒ a + 2 = 0
⇒ a = 0 - 2
⇒ a = -2
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