Question

Given that X square + 2 x minus 3 is a factor of f x is equal to X ki power 4 + 6 x cube + 2 X square + bx - 3 find the value of a and b

Answer 1

here is your answer
Thanks for asking

Answer 2

Answer:

The value of b is -6

Step-by-step explanation:

Given $x^2+2x-3$ is a factor of $x^4+6x^3+2x^2+bx-3$

We have to find the value of b

Therefore the zeroes of the given factor also the zeroes of the given polynomial.

The zeroes of  $x^2+2x-3$ are

$x^2+2x-3=0$

$x^2+3x-x-3=0\\\\x(x+3)-1(x+3)=0\\\\(x-1)(x+3)=0\\\\x=1, x=-3$

As $x^2+2x-3$ is a factor of $x^4+6x^3+2x^2+bx-3$

∴ x=1 and x=-3 are also the roots of given polynomial

$x^4+6x^3+2x^2+bx-3$

⇒ $(1)^4+6(1)^3+2(1)^2+b(1)-3=0$

⇒ b=-6