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फ़ोरम
if a & b are the roots of a quadratic equation 2x^2 + 6x + k = 0, where k<0, then what is the maximum value of (a/b)+(b/a) ?
Answer

if a & b are the roots of a quadratic equation 2x^2 + 6x + k = 0, where k<0, then what is the maximum value of (a/b)+(b/a) ?

with solution plz

Deep
25 अगस्त
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Your Answer

Shruti
24 अगस्त

Let r be the lesser root and r^2 be the greater.......the sum of the roots = -b/a = -[-6] / 1 = 6

So we have that

r^2 + r = 6 → r^2 + r - 6 = 0

Factor

(r + 3) (r - 2) = 0

So r = -3 or r = 2

Then r^2 = 9 or r^2 =4

And the product of the roots = c/a = k/a = k

So....k = (-3)(9) = -27 or k = (2)(4) = 8

Check

x^2 - 6x - 27 = 0 factors as (x + 3)(x - 9) = 0 and the roots are -3 and 9

x^2 - 6x + 8 = 0 factors as (x -2) (x - 4) =0 and the roots are 2 and 4