If α and β are roots of x2 + mx - n = 0, ...
If α and β are roots of x2 + mx - n = 0, where m and n are constants, form the
| equation | whose | roots | are | 1
α |
and | 1
β |
. |
mnx2 - n2 x - m = 0
mx2 - nx + 1 = 0
nx2 - mx + 1 = 0
nx2 - mx - 1 = 0
Correct answer is D
x2 + mx - n = 0
a = 1, b = m, c = -n
α + β = −ba = −m1 = -m
αβ = ca = −n1 = -n
the roots are = \frac{1}{α} and \frac{1}{β}
sum of the roots = \frac{1}{α} + \frac{1}{β}
\frac{1}{α} + \frac{1}{β} = \frac{α+β}{αβ}
α + β = -m
αβ = -n
\frac{α+β}{αβ} = \frac{-m}{-n} → \frac{m}{n}
product of the roots = \frac{1}{α} * \frac{1}{β}
\frac{1}{α} + \frac{1}{β} = \frac{1}{αβ} → \frac{1}{-n}
x^2 - (sum of roots)x + (product of roots)
x^2 - ( m/n )x + ( 1/-n ) = 0
multiply through by n
nx^2 - mx - 1 = 0
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