Question

group consists of 12 honest people and 8 dishonest people. Write a quadratic polynomial whose roots are equal to number of honest people and number of dishonest people. Which value do you prefer ?

Answer 1

Solution :-

Number of honest people in the group = 12

Number of dishonest people in the group = 8

Now,

Let the two given values be α and β, where α = 12 and β = 8 respectively.

Now, sum of the roots = α + β 

= 12 + 8

Sum of the roots = 20

And, product of the roots = α × β

= 12 × 8

Product of the roots = 96

Therefore, the quadratic polynomial will be -

p(x) = x²(Sum of the roots)x + Product of the roots

p(x) = x²(12 + 8)x + (12 × 8)

p(x) = x² = 20x +  96

The required polynomial is x² + 20x + 96

Answer.

Answer 2

Answer:

Refer to the attachment...