Question

if alpha and beta are the roots of the equation 2x^2 - x - 1=0, then form the equation whose roots are 1/alpha, 1/beta ​

Answer 1

2x²- x- 1=0

2x²-2x+x-1=0

2x(x-1)+1(x-1)=0

(2x+1)(x-1)=0

x=-1/2  or x=1

α=-1/2  and β=1

1/α= -2  and 1/β=1

FORMULA FOR FINDING EQUATION:

x²-(sum of roots)x + (product of roots)=0

x²- (-2+1)x + (-2×1)=0

x²-(-1)x + (-2)=0

x²+ x-2=0

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