Question

$Find \: the \: value \: of \\ \: a \: for \: which \: (x + 1) \: is \: a \: factor \\ \: of \: (a {x}^{3} + {x}^{2} - 2x + 4a - 9 \\ \\ please \: solve \: it \: and \: the \: answer \: is \: \\ a = 2$
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Answer 1

Answer:

2

Step-by-step explanation:

given equation,

p(x) = ax³ + x² - 2x + 4a - 9

and x + 1 is the factor of p(x)

then zero => x + 1 = 0

x = -1

since -1 is the zero of p(x) so,

p(-1) = 0

now,

putting -1 at the place of x

a(-1)³ + (-1)² - 2(-1) + 4a - 9 = 0

-a + 1 + 2 + 4a - 9 = 0

-a + 4a - 6 = 0

3a = 6

a = 6/3

a = 2

so, the required number a = 2

hope it helps

Answer 2

Step-by-step explanation:

p(x)=ax³+x²-2x+4a-9

and x+1is a factor of this

so x+1=0

x=-1

now putting the value of x in p(x)=ax³+x²-2x+4a-9

p(-1)=a(-1)³+(-1)²-2(-1)+4a-9

p(-1)=-1a+1+2+4a-9

p(-1)=3a-6=0

a=6/3=2