Question

If the sum of the zeros of the quadratic polynomial f(t) = kt² + 2t + 3k is equal to their product, find the value of k.

Answer 1

let the zeroes be p and q

sum of roots = b/a

p+q=b/a

product of roots =c/a

pq=c/a

sum = product

b/a=c/a

where from the equation f(t)=kit^2+2t+3k is in the form of ax^2+bx+c=0 where a=k b=2 c=3k

2/ k=3 k/k

2/k =3

the value of k= 2/3

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