Hi...

You have gone wrong on calculating SUM of roots...

Product of roots = c/a=64=a*b.....

SUM of roots =-b/a=-16=a+b

So both a and b are -8

Hi

chetan2u Many thanks for your kind explanation. Let me summarize my knowledge of quadratic equation

Please read below. It is only 1 minute read

Here is formula of quadratic:

ax^2 + bx + c = 0

Discriminant (D) = B^2-4Ac

Find roots:

X1 = -B+ sqrt D/ 2a

X2 = -B- sqrt D/2a

In our case, discriminant is equal to 0 (zero)

Hence:

x1 = -16+0/2 = - 8

X2 = -16-0/2 = -8

So both roots are equal to -8 ---> Correct?

Now lets solve the same problem through factorization

(x+a) (x+b)= 0

X^2+bx+ax+ab = 0

X^2+x (a+b)+ab = 0

Now let`s get back to our case:

X^2y+16xy+64y = 0

Y (X^2+16+64) = 0

A is X^2

B is 16

C is 64

So 64 is our C term

The numbers that can multiply to make 64 are +8 and +8 (8*8 = 64)

16 is our B term

Now find the two factors of C that add up to your B term 8 and 8 Hence 8+8 = 16

Now plug in values I have chosen into factored equation (x+a) (x+b)= 0

(x+8) (x+8)= 0

Now solve for X by equating to 0

(x+8) =0 ---- > x = -8

(x+8)= 0 ----- >x = - 8

Is my understanding now correct ? So both roots are -8 (What if one eight is negative and other eight root is positive ? like this: -8 and +8 does it mean that equation has 2 roots ?

If my understanding is correct what role does Y play i our case ?

Thank you SO much !

Highly appreciated.