Question

if alpha and beta are the zeroes of the quadratic polynomial of f(x)=x^2+x-2,find the value of 1/α-1/β

Answer 1

Hello!

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= x² + x - 2 = 0

= x² + 2x - x - 2 = 0

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

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

= x = 1, -2

Let @ = 1 and β = -2 (My keyboard does not have alpha symbol so let alpha symbol be @)

= 1/ @ - 1/ β

We will take the LCM.

= (β - @) / @β

= (-2 - 1) / -2(1)

= -3 / -2

= 3/ 2

Therefore, the value of 1/@ - 1/β = 3/2.

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I hope it helped.

Thank You!