Question

Find a quadratic polynomial whose zeroes are `(5 - 2sqrt3) and (5 + 2sqrt3)`.

Answer 1

Let the α = `(5 - 2sqrt3)` and β = `(5 + 2sqrt3)`.

Sum = α + β

= `(5 - 2sqrt3) + (5 + 2sqrt3)`

= `5 - 2sqrt3 + 5 + 2sqrt3`

= 5 + 5

=10

Product = `α * β`

= `(5 - 2sqrt3) * (5 + 2sqrt3)`

= `(5)^2 - (2sqrt3)^2`

= 25 − (4 x 3)

= 25 − 12

= 13

A quadratic polynomial with sum S and product P is given by x² − Sx + P.

p(x) = x² − (10)x + 13

∴ The quadratic polynomial is x² − 10x + 13.