Question

Obtain a quadratic polynomial whose sum of the zeros is 2 and product of zeros is
-3.​

Answer 1

Step-by-step explanation:

Let α and β be the zeros of the polynomial p(x) = ax2 + bx + c.

Given, α + β = 2 ; αβ = –3

We know that α + β = – = – . So, – = = k, say

Thus, b = –2k, a = k

And αβ = = – . So, c = –3a = –3(k) = –3k

p(x) = ax2 + bx + c

∴ p(x) = (k)x2 + (–2k)x – 3k

∴ p(x) = k (x2 – 2x – 3)

Answer 2

Step-by-step explanation:

sum of zeroes=2/1= -b/a= coefficient of x/coefficient of x2

product of zeroes =-3/1=c/a=constant term /coefficient of x2

a=1,b=-2,c=-3

quadratic polynomial= (ax)2+bx+c

=(1×x)2+(-2)x+. (-3)=x2-2x-3