Question

If xalpha=5& ß = -2 find the polynomial​

Answer 1

Answer:

x² - 3x - 10

Solution:

Given :

α = 5

ß = -2

To find :

A polynomial whose zeros are α and ß.

We know that ,

If α and ß are the zeros of a quadratic polynomial , then the polynomial is given as ;

x² - (α+ß)x + αß

Here,

α = 5

ß = -2

Sum of zeros = α + ß

= 5 + (-2)

= 5 - 2

= 3

Product of zeros = αß

= 5•(-2)

= -10

Hence,

The required polynomial will be;

x² - (α+ß)x + αß

ie; x² - 3x + (-10)

ie; x² - 3x - 10

Hence,

Tbe required polynomial is :

x² - 3x - 10