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.