Find the value of a, if x - 1 is a factor of x³ - ax² + 2x + a− 1.
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0
Answer:
Given,
x - a is a factor of
{x}^{3} - ax {}^{2} + 2x + a - 1x3−ax2+2x+a−1
we know,
x - a = 0
x = 0+a = a
Substitung the value of x as a,
we have,
(a)^3 - a(a)^2 + 2(a) + a - 1 =0
a^3 - a^3 + 2a + a - 1=0
3a - 1=0
3a =1
a = 1/3
Thus
a = 1/3
Answered by
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Since, x+1 is a factor of p(x)=2x
3
+ax
2
+2bx+1
Then, by factor theorem, p(−1)=0
⇒−2+a−2b+1=0⇒a−2b=1 ...(i)
Also,2a−3b=4 ...(ii)
On multiplying (i) by 2 and (ii) by 1, we get
2a−4b=2
−
2
a
+
−
3b=
−
4
−b=−2
∴b=2
On putting b=2 in (i), we get
a−2×2=1⇒a=5
∴a=5,b= 2
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