Question

How many polynomials can be formed with the zeroes 2and (-3)?​

Answer 1

let the polynomial be

$p(x) =ax^2 +bx+c\\Sum of zeroes =2\\-\frac{b}{a}=2\\a =1\\\\-\frac{b}{1} =2\\-b=2\\b= -2\\product of zeroes = -3\\\frac{c}{a} =-3\\\frac{c}{1} =-3\\c=-3$

Answer 2

Given,

Zeros of the polynomial $\[{\rm{ = 2, - 3}}\]$

Solution,

Consider the variable is x.

First zero,

$\[\begin{array}{l}{\rm{x = 2}}\\ \Rightarrow {\rm{x - 2 = 0}}\end{array}\]$

Second zero,

$\[\begin{array}{l}{\rm{x = - 3}}\\ \Rightarrow {\rm{x + 3 = 0}}\end{array}\]$

Multiply both equations obtain from zeros.,

$\[\begin{array}{l}\left( {{\rm{x - 2}}} \right)\left( {{\rm{x + 3}}} \right){\rm{ = 0}}\\ \Rightarrow {x^2}{\rm{ - 2x + 3x - 6 = 0}}\\ \Rightarrow {x^2}{\rm{ + x - 6 = 0}}\end{array}\]$

Hence there is only 1 polynomial $\[{x^2}{\rm{ + x - 6 = 0}}\]$ formed.