Question

Find the quadratic polynomial whose zeros and minus 4 and 3 and verify the relationship between the zeros and the coefficient

Answer 1

Answer:

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=-4 and β=3,

So the equation becomes

(X-(-4))(X-3)=0

(X+4)(X-3)=0

Open the terms by multiplying

X²+X-12=0

This is your answer.

Relationship between zeroes and coefficients:

General quadratic equation

aX²+bX+C=0

We have X²+X-12=0

On comparing,we get a=1,b=1,c=-12

As we know,

Sum of roots =α+β=-4+3=-1 (which is also equal to -b/a=-1/1=-1)

Product of roots=α×β=-4×3=-12(which is also equal to c/a=-12/-1=-12)

Hence,verified

Thank you