Question

find the quadratic polynomial whose zeroes are -3 and 2​

Answer 1

Idea

• Factor Theorem

The polynomial has (x+3) and (x-2) as the two factors.

Solving

A polynomial with both factors will be

$\sf{(x+3)(x-2)=x^2+(3-2)x+(3)\times(-2)}$

$\sf{=x^2+x-6}$

If we consider its highest coefficient

∴$\sf{k(x^2+x-6)}$ (k is a number which is not 0)

For your information.

• The Relation between Roots and Coefficients
• Factor Theorem

The first one can be shown by the second one.

(Or by the quadratic formula.)

(showing)

Let two zeros be α and β.

By factor theorem,

their factors will be (x-α) and (x-β).

$\sf{(x-\alpha)(x-\beta)=x^2-(\alpha +\beta )+\alpha \times\beta }$

Therefore it is shown.