Question

Find the value of 'a' if x-1 is a factor of p(x)=4x³+3x²-4x+a

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Answer 1

Step-by-step explanation:

Let P(x)=4x

3

+3x

2

−4x+k

Given, (x−1) is a factor of P(x)

x−1=0

x=1∴ p(1)=4×(1)

2

+3×(1)

2

−4×(1)+k=0

4+3−4+k=0

k+3=0

k=−3

Hence, the value of k is −3.

Answer 2

Required Answer :-

• In the question we have to Find the value of 'a'

• If x-1 is a factor of p(x)=4x³+3x²-4x+a

so ,

${\sf{:\implies x - 1 = 0 }}$

${\sf{:\implies x = 1}}$

Now ,

${\sf{:\implies p(x) = {4x}^{3} + {3x}^{2} - 4x + a }}$

by putting the value of x as 1

${\sf{:\implies p(1) = {4(1)}^{3} + {3(1)}^{2} - 4(1) + a }}$

${\sf{:\implies p(1) = {4} + {3} - 4+ a }}$

${\sf{:\implies p(1) = 3+ a }}$

${\sf{:\implies 0= 3+ a }}$

${\sf{:\implies a= - 3 }}$