Question

Find the quadratic polynomial, the sum of whose zeros is 5/2 and their
product is 1. Hence, find the zeros of the polynomial.​

Answer 1

Answer:

sum of zeroes : alpha + beta = -b/a

so we can say that -b/a = 5/2

so value of b is -5 and that of a is 2.

product of zeroes :

alpha x beta = c/a

product =1

so c =?

Answer 2

Step-by-step explanation:

Quadratic polynomial -

x² - (Sum of zeroes)x + (product of zeroes) = 0

x² - (5/2)x + 1 = 0

2x² - 5x + 2 = 0

Let the zeroes are x & y .

So , x + y = 5/2 --------(1)

xy = 1

x - y = √(x + y)² - 4xy

x - y = √(5/2)² - 4(1)

= √(25/4) - 4

= √(25-16)/4

= √9/4 = 3/2

x - y = 3/2 --------(2)

from equation (1) + (2)

2x = 8/2 = 4

x = 2

y = 5/2 - 2 = 1/2

So , the zeroes of above polynomial are 2 & 1/2 .