Question

Find the quadratic polynomial whose zeros are given as 2 and -1.

Answer 1

Let the quadratic  polynomial be

ax² + bx + c = 0 and its zeroes be 

α = 2 and β = −1

Sum of the zeroes = α + β

= 2 + (−1)

= 2 − 1

= 1

Product of the zeroes = αβ

= 2 × (−1)

= −2 

The quadratic polynomial  will be

ax² + bx + c is 

k[x² − (α + β)x + αβ]

k[x² − (1)x + (−2)]

If K = 1 , the quadratic polynomial will be

1[x² − (1)x + (−2)]

⇒ x² − x − 2