Question

Alpha and 1/alpha are the zeroes of the polynomial 3x^2 +x+ (k-2) find k

Answer 1

please see the attachment

Answer 2

Step-by-step explanation:

Given-

α and 1/α are the zeros of a polynomial

p(x)= $3x^{2} +x+(k-2)$

which is in the quadratic form

$ax^{2} +bx+c$

here a=3, b=1 and c=k-2

If we see the relation of zeros

$\alpha +1/\alpha$ = -b/a = -1/3

α × 1/α = c/a = k-2/3

we have to find k so we take the 2nd relation i.e.,

α × 1/α = k-2/3

α and α get cancelled

1 = k-2/3

multiplying by 3 we get

1 x 3 = k-2/3 x 3

3 and 3 get cancelled,  we get

3 = k-2

or

k-2 = 3

so,

     k = 3 + 2

     k = 5

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