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if alpha = −1/2 is a root of the quadratic equation 8x 2 − bx− 3 = 0 find the value of b the other root beta (1/alpha−1/beta) 2

if alpha = −1/2 is a root of the quadratic equation 8x2 − bx− 3 = 0 find the value of 
  1. b
  2. the other root beta
  3. (1/alpha−1/beta)2

Grade:11

1 Answers

Arun
25750 Points
6 years ago
If alpha = -1/2 is a root hence alpha  should satisfy this quadratic equation
Put x = -1/2
8* 1/4  +b/2 -3 = 0
b/2 = 3-2
b/2 = 1
Hence 
b = 2
Now equation becomes
8x² -2x-3 = 0
Then by formula 
x = 12/16 = 3/4 & x = -1/2
Hence 
Beta = ¾
Now
(1/alpha - 1/beta)²
= (-2 -4/3)²
 = 100/9
Hope it helps
May be calculation mistake is lresent somewhere but concept is right

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