Question
Sat October 20, 2012 By: Arnav Sharma

if x is root 2 and it is a solution of quadratic equation x*+kx-4=0 then find the value of k ?

Expert Reply
Sat October 27, 2012
Answer : Given : x = 21/2 and it is a solution of quadratic equation x2+kx-4=0
To find : the value of k
 
=> x2+ kx - 4 = 0
is a quadratic equation where a = 1 , b = k , c = -4
D = b2 - 4ac
    = k2 - 4(1)(-4)
    = k2 + 16
 
x = (-b + D1/2 ) / 2a and x = (-b - D1/2 ) / 2a
 
x= ( -k + ( k2 + 16)1/2 ) /2
since x = 21/2 given , therefore
=> ( -k + ( k2 + 16)1/2 ) /2 = 21/2
=>  -k + ( k2 + 16)1/2  = 2 ( 21/2)
=>  ( k2 + 16)1/2 2 ( 21/2) + k 
squaring both the sides, we get
 
=>  k2 + 16  = (2 ( 21/2) + k )2
=>  k2 + 16 = 8 + k2 + 4k(21/2) { applying (a+b)2 = a2 +b2 + 2ab }
 
=> 4k(21/2) = 8 
=> k(21/2) = 2 
=> k = 21/2 Answer 
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