Question

If sum of the squares of zeroes of the quadratic polynomial 6x2 + x + k is 25/36, the value of k is:

Answer 1

let a and b be the zeroes of the given polynomial.

a^2+b^2=25/36

sum of zeroes=a+b=-b/a =-1/6

product of zeroes=ab=c/a=k/6

(a+b)^2=a^2+b^2+2ab

(-1/6)^2=25/36+2(k/6)

1/36=25/36+k/3

1/36-25/36=k/3

-24/36=k/3

-2/3=k/3

k=-2

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