Question

If ax + bx+c and bx2 + ax + c have a common factor x + 1 then show that
c=0 and a=b.​

Answer 1

Answer:

a = b & c = 0

Step-by-step explanation:

If ax2+bx+c and bx2+ax+c have a common factor x+1 then show that c=0 a=b

ax² + bx + c = (x + 1)(dx + e)

=> ax² + bx + c = dx² + (d + e)x + e

=> d = a e = c & b = d + e = a + c

b = a + c

bx² + ax + c = (x + 1)(fx + g)

=> bx² + ax + c = fx² + (f + g)x + g

=> f = b g = c a = f + g = b + c

a = b + c

adding both

b + a = a + b + 2c

=> 2c = 0

=> c = 0

putting this in above

a = b

hence,proved....