Question

Example 4 :Find a quadratic polynomial, the sum and product of whose zeroes are
- 3 and 2, respectively.​

Answer 1

This is your answer :
Answer -: x^2 + 3x +2
Given : the sum and product of the zeroes are -3 and 2 respectively.

To proof : quadratic polynomial

Let the quadratic polynomial be ax^2+bx+c and it's zeroes be Alpha and beta .

Proof:

Given that ,

Alpha + beta = -3
Alpha +beta = -b/a
-3 = -b/a
a = 1 b = 3

Given ,
Alpha*Beta = c/a
Alpha beta = 2
C/a = 2 (Since , a is 1)
c =2

Now , the quadratic polynomial is ax^2 +bx + c
Putting all the values , we get
Ans : x^2 +3x +2


Thankyou !! Good luck