CBSE Class 10 Answered
if x is root 2 and it is a solution of quadratic equation x*+kx-4=0 then find the value of k ?
Asked by arnav sharma | 20 Oct, 2012, 10:32: AM
Expert Answer
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
Answered by | 27 Oct, 2012, 07:07: PM
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