Question

1/x+a + 1/x = 1/k+a + 1/k has two roots which are equal in magnitude but opposite in sign. then 'a' is equal to​

Answer 1

Answer:

Converting the above given equation into standard quadratic form i.e Ax^2 + Bx + C and comparing its co-efficients we get

A = 2k + a,

B = a^2 - 2k^2,

C = -ak^2 - ka^2,

Let the roots of the equation be x1 and x2.

As it is said that the roots are equal but opposite in sign which implies that,

x1 + x2 = 0.

we know that addition of two roots of quadratic equation is equal to -B/A.

Thus we can conclude that x1 + x2 = -B/A = 0

i.e. B = 0

a^2 - 2k^2 = 0

a^2 = 2k^2

i.e. a = +-sqrt(2)k.

Step-by-step explanation:

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