Question

Give the polynomial of degree 2 with sum and product of its

zeros are – 1/2 and - 3 respectively.​

Answer 1

Answer:

let the equation is ax^2+bx+c

if p and q are roots of equation

then p+q=-b/a=-1/2. eq (1)

and p×q=c/a=-3. eq (2)

so.

comparing equation 1and equation 2

We get

a=2; b=1;c=-6

2x^2+x-6=0

Answer 2

Given: The polynomial is of degree 2 and the sum and product of its zeros are -1/2 and -3 respectively

To find: The polynomial

Explanation: Let the sum of zeroes be denoted by s and product of its zeros be denoted as p.

Therefore, p= -3 and s= -1/2

The expression of a polynomial whose sum and product of its zeros are known is given by:

${x }^{2} - sx + p$

Using the known values:

${x}^{2} - ( \frac{ - 1}{2} )x + ( - 3)$

${x}^{2} + \frac{1}{2} x - 3$

This is a polynomial with degree 2 as the highest power of the variable is 2.

Therefore, the polynomial with degree 2 whose sum and product are -1/2 and -3 respectively is ${x}^{2} + \frac{1}{2} x - 3$.