Question

• If alpha and beta are the zeros of quadratic polynomial x² + x - 2
then find the value of (1/alpha-1/beta)​

Answer 1

Answer:

1.5

Step-by-step explanation:

α+β=-1

αβ=-2

(α-β)^=(α+β)^-4αβ

=-1^-4(-2)

=1+8

=9

α-β=3

By simplification we get as

α=1 &β=-2

1/α-1/β=1-(-1/2)

=1+1/2

=3/2

=1.5

Answer 2

Answer:

Answer is 3/2

Step-by-step explanation:

If alpha and beta are the zeros of given polynomial,

x^2 + x + 2 = 0

=> x^2 + 2x - x -2 = 0

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

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

Therefore, x = 1, -2

Thus, 1/1 - 1/-2 = 1 + 1/2 = 3/2

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