Question

if a≠band the difference between the roots of the polynomials x^2+ax+b and x^2 +bx+a is the same ,then, (1) a+b+4=0.. (2) a+b-4 = 0.. (3) a- b +4 =0..(4) a-b -4=0... which is correct​

Answer 1

Answer:

a + b  - 4 = 0

Step-by-step explanation:

The roots of the equation x2 + ax + b are:-

[-a + root(a2 -4b)]/2 and [-a - root(a2 -4b)]/2

Hence their difference  = root(a2 -4b)/2

The roots of the equation x2 + bx + a are:-

[-b + root(b2 -4a)]/2 and [-b - root(b2 -4a)]/2

Hence their difference  = root(b2 -4a)/2

As we know their difference is equal then

root(b2 -4a)/2 = root(a2 -4b)/2

root(b2 -4a) = root(a2 -4b)

(b2 -4a) = (a2 -4b)

4a - 4b = a2 - b2

4(a - b) = (a - b) (a + b)

4 = a + b

a + b -4 = 0