Question

If alpha and beta are the zeros of the quadratic polynomial f(x)=6x2+x_2 find the value of alpha /beta +beta/alpha​

Answer 1

a=6;b=1;c=-2(given)

we know that alpha + beta =-b/a=-1/6 (1)

(alpha)(beta)=c/a=-2/6=-1/3.....(2)

so according to question we have

alpha/beta+beta/alpha

(alpha)^2+(beta)^2/(alpha)(beta)

(L.C.M.=alpha×beta)

{(a)^2+(b)^2= (a+b)^2 - 2ab......(3) }

so from (3) we have

(alpha +beta)^2 -2(alpha)(beta)

from (1) & (2) we have

(-1/6)^2 -2(-1/3)

1/36 + 2/3 (L.C.M.=36)

1+24/36

25/36 is the value of

alpha/beta +beta/alpha

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