Question

Heyy Mathematicians !!!

Help Plz

Class X polynomials

Q. Find the values of a and b so that
${x}^{4} + {x}^{3} + 8 {x}^{2} + ax + b$
is exactly Divisible by x^2 +1


BRAINLIEST for sure​

Answer 1

x = + 1

1^4+1³+8(1)²+a(1)+b =0

1+1+8+a+b =0

10 + a+b =0

a + b = -10

..........

Answer 2

Answer:

a = 1, b = 7

Step-by-step explanation:

Given: f(x) = x⁴ + x³ + 8x² + ax + b

Given: g(x) = x² + 1

Divide f(x) by g(x):

Long Division Method:

x² + 1) x⁴ + x³ + 8x² + ax + b(x² + x + 7

          x⁴        + x²

          ---------------------------------

                 x³ + 7x² + ax + b

                 x³           + x  

           --------------------------------------

                        7x² + x(a-1) + b

                        7x²              + 7

             ------------------------------------

                              x(a - 1) + (b - 7)

∴ Remainder = 0

⇒ x(a - 1) + (b - 7) = 0

⇒ (a - 1) = 0, (b - 7) = 0

⇒ a = 1, b = 7

Hope it helps!