Answer :

mbharavi5

Answer:

Hey!

  • To find the value of "a" if (x+1) is a factor of ax³+x²-2x+4a-9, we can use the factor theorem. According to the factor theorem, if (x+1) is a factor of a polynomial, then the polynomial will be equal to zero when we substitute (-1) for x.
  • So, let's substitute (-1) for x in the given polynomial:
  • (-1)³ + (-1)² - 2(-1) + 4a - 9 = 0
  • Simplifying this equation will help us find the value of "a".

Step-by-step explanation:

Sure, let's solve it together!

When we substitute (-1) for x in the polynomial, we get:

(-1)³ + (-1)² - 2(-1) + 4a - 9 = 0

Simplifying this equation:

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

Combining like terms:

4a - 7 = 0

To isolate "a", we can add 7 to both sides of the equation:

4a = 7

Finally, we can solve for "a" by dividing both sides of the equation by 4:

a = 7/4

So, the value of "a" is 7/4.

GeniusYH

Answer:

a = 2

Step-by-step explanation:

Hello dear friend,

Theorem:

To find the value of [tex]\(a\)[/tex], we'll use the factor theorem, which states that if [tex]\( (x - r) \)[/tex] is a factor of a polynomial, then [tex]\( r \)[/tex] is a root of the polynomial.

Solution:

Given that [tex]\( (x + 1) \)[/tex] is a factor of [tex]\( ax^3 + x^2 - 2x + 4a - 9 \)[/tex], we know that when [tex]\( x = -1 \)[/tex], the polynomial evaluates to zero.

So, let's substitute [tex]\( x = -1 \)[/tex] into the polynomial:

[tex]\[ a(-1)^3 + (-1)^2 - 2(-1) + 4a - 9 = 0 \][/tex]

Simplify and solve for [tex]\(a\)[/tex]:

[tex]\[ -a + 1 + 2 + 4a - 9 = 0 \][/tex]

[tex]\[ 3a - 6 = 0 \][/tex]

[tex]\[ 3a = 6 \][/tex]

=> [tex]\[ a = \frac{6}{3} \][/tex]

Hence, [tex]\[ a = 2 \][/tex]

So, the value of [tex]\( a \)[/tex] is [tex]\( 2 \)[/tex].

I hope you have understood my explanation and felt it was somewhat helpful to you.

Have a great day ahead !

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