Question

If (x-2) is a factor of x3 + ax ²+bx+ 8
and a-b=7 find a and b.​

Answer 1

Answer:

a=5 b=2

Step-by-step explanation:

i hope helpful rahe plz follow for more answers

Answer 2

Answer:

$a = \frac{ - 1}{3}$

$b = \frac{ - 22}{3}$

Step-by-step explanation:

$p(x) = {x}^{3} + {ax}^{2} + bx + 8$

Since x-2 is a factor of p(x)

→x=2

So,

$p(2) = {(2)}^{3} + {a(2)}^{2} + b(2) + 8$

$8 + 4a + 2b + 8$

Which gets us

$4a + 2b + 16$

We can also write this as

$4a + 2b = - 16 \\ (1)$

Also,

$a - b = 7 \\ (2)$

Multiplying (2) with 2

$2a - 2b = 14 \\ (3)$

Adding (2) and (3)

$6a = - 2$

We can also write this as

$a = \frac{ - 2}{6}$

$a = \frac{ - 1}{3}$

Substituting this value in (2)

$\frac{ - 1}{3} - b = 7$

$\frac{ - 1 - 3b}{3} = 7$

$- 1 - 3b = 7 \times 3$

$- 3b = 21 + 1$

$b = \frac{ - 22}{3}$

So,

$a = \frac{ - 1}{3}$

$b = \frac{ - 22}{3}$

I may not be correct. So please verify the answer and let me know if this is incorrect.