Question

Find a quadratic polynomial, the sum and product of whose zeroes are √3

and 1

√3

respectively​

Answer 1

Answer:

x²-x+√3

Step-by-step explanation:

Let the polynomial be ax²+bx+c=0

The rules of quadratic eqn say that the sum of the zeroes = -b/a and product is c/a

If p and q are the zeroes of the polynomial,

p + q = -b/a = 1 (given) => b=(-a)

and p×q = c/a = √3 (given) => c=a√3

So, the polynomial can be written as (kx²-kx+ k√3), where k is a constant.

It is likely x²-x+√3 where k=1