Question

please give the answer fast​

Answer 1

Step-by-step explanation:

$\huge\underline{\underline{Question}} \\ {x}^{4} + a {x}^{3} - 7 {x}^{2} + 8x + b \\ is \: exactly \: divisible \: by = > \\ \: x = - 2 \: and \: x = - 3$

$\huge\underline{\underline{Answer}}$

So,

x = -2 , -3

will satisfy the equation...

$x {}^{4} + a {x}^{3} - 7 {x}^{2} + 8x + b = 0$

put x = -2

$16 - 8a - 28 - 16 + b = 0 \\ 8a - b = - 28.......(1)$

now put x = -3

$81 - 27a - 63 - 24 + b = 0 \\ - 27a + b = 6.......(2)$

Add (1) + (2) =>

$- 19a = 18 \\ a = \frac{ - 18}{19}$

$b = 6 - \frac{27 \times 18}{19}$