Question

If ax?+bx+3 = 0 and 2x² +8x+6=0 have both roots common, then b:a​

Answer 1

Answer:

Hi, I am putting this answer assuming that the "?" you have put in first equation is square, if it is something else, please let me know

Step-by-step explanation:

2x²+8x+6=0

2x²+2x+6x+6=0

2x(x+1)+6(x+1)=0

(2x+6)(x+1)=0

x=(-1),(-3)

ax²+bx+3=0

Substituting x=-1,

a-b+3=0

a-b=-3

b-a=3         ...(i)

ax²+bx+3=0

Substituting x=-3,

9a-3b+3=0

3b-9a=3

b-3a=1           ...(ii)

Subtracting eq(ii) from eq(i),

b-3a=3

-b+a=-1

______

2a=2

a=1                         ...(iii)

Multiplying eq(ii) by 3,

3(-b+a)=(-1*3)

-3b+3a=-3        ...(iv)

Subtracting eq(iv) from eq(i),

  b-3a= 3

-3b+3a=-3

________

-2b=0

b=0

Therefore, b:a::0:1