If α and β are roots of $x^2 + mx - n = 0$,... | WAEC SSCE - Further Mathematics - 2022

Question 1 Report

If α and β are roots of $x^2 + mx - n = 0$, where m and n are constants, form the

equation

whose

roots

are

1α

and

1β

mnx

^{2}

- n

^{2}

x - m = 0

^{2}

- nx + 1 = 0

^{2}

- mx + 1 = 0

^{2}

- mx - 1 = 0

Answer Details

x $^{2}$ + mx - n = 0

a = 1, b = m, c = -n

α + β = $\frac{- b}{a}$ = $\frac{- m}{1}$ = -m

αβ = $\frac{c}{a}$ = $\frac{- n}{1}$ = -n

the roots are = $\frac{1}{α}$ and $\frac{1}{β}$

sum of the roots = $\frac{1}{α}$ + $\frac{1}{β}$

$\frac{1}{α}$ + $\frac{1}{β}$ $\frac{α + β}{α β}$

α + β = -m
αβ = -n

$\frac{α + β}{α β}$

product of the roots = $\frac{1}{α}$ * $\frac{1}{β}$

$\frac{1}{α}$ + $\frac{1}{β}$ = $\frac{1}{α β}$ → $\frac{1}{- n}$

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

If α and β are roots of \(x^2 + mx - n = 0\), where m and n are constants, form the equation whose roots are 1α and 1β .