Question

જો બહુપદી x + 5x³ + 11x² + 15x + 15ને બીજી
બહુપદી x² + 2x + k વડે ભાગવામાં આવે, તો શેષ
2x + a મળે છે. k અને a શોધો.​

Answer 1

Answer:

k=3 and a=9

Step-by-step explanation:

p(x) = x^4 + 5x^3 + 11x^2 + 15x +15

g(x) = x^2 + 2x + k

r(x) = 2x + a

if you divide them, you'll get this :

q(x) = x^2 + 3x + (5-k)

r(x) = (5-k)x + k^2 - 5k + 15

from given r(x) :

r(x) = r(x)

2x + a = (5-k)x + k^2 - 5k + 15

so that, 2x = (5-k)x and also a = k^2 - 5k + 15

2x = 5x - kx

2x - 5x = - kx

-3x = - kx

so that -3 = -k

and k=3

put k = 3 in k^2 - 5k + 15 = (3)^2 - 5(3) + 15

so its 9-15+15 = 9

so a = 9