If the roots of 16x2 - 1 + x - kx = 0 , are mutually opposite then find k. step by step
Answers
Answer:
K=1
Step-by-step explanation:
16x2-1+x-kx=0
16x2+(1-k)x-1=0
by trial method if we take k=1
16x2-1=0
(4x)2-(1)2 i.e (a) 2-(b) 2=(a+b)(a-b)
(4x+1)(4x-1)=0
4x+1=0 4x-1=0
x=-1/4 x=1/4
hence proved roots are opposite
Given : roots of 16x² - 1 + x - kx = 0 , are mutually opposite
To Find : Value of k
Solution:
16x² - 1 + x - kx = 0
=> 16x² + x(1 - k) - 1 = 0
Let say roots are α & -α
Sum of roots = α -α = - (1-k)/16
=> 0 = - (1-k)/16
=> k = 1
16x² - 1 = 0
=> x² = 1/16
=> x = ± 1/4
α = 1/4
Value of k = 1
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