Question

what is the umber of polynomials having zeros -2 and 5?

Answer 1

nswer:

X²+X-12=0

Step-by-step explanation:

A quadratic polynomial with roots(zeroes) α and β can be written as

(X-α)(X-β)=0

Here, α=-2 and β=5,

So the equation becomes

(X-(-2))(X-5)=0

(X+2)(X-5)=0

Open the terms by multiplying

X²-3X-10=0

This is your answer.

Relationship between zeroes and coefficients:

General quadratic equation

aX²+bX+C=0

We have X²-3X-10=0

On comparing,we get a=1,b=-3,c=-10

As we know,

Sum of roots =α+β=-2+5=3

Product of roots=α×β=-2×5=-10