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

1 答案

Let r be the lesser root and r^2 be the greater.......the sum of the roots = -b/a = -[-6] / 1 = 6br / br /So we have thatbr / br /r^2 + r = 6 → r^2 + r - 6 = 0 br / br /Factorbr / br /(r + 3) (r - 2) = 0 br / br /So r = -3 or r = 2br / br /Then r^2 = 9 or r^2 =4br / br /And the product of the roots = c/a = k/a = kbr / br /So....k = (-3)(9) = -27 or k = (2)(4) = 8br / br /Checkbr / br /x^2 - 6x - 27 = 0 factors as (x + 3)(x - 9) = 0 and the roots are -3 and 9br / br /x^2 - 6x + 8 = 0 factors as (x -2) (x - 4) =0 and the roots are 2 and 4
- Shruti
- 24 8月
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