Question

Write a quadratic polynomial whose one zero is 3-√5 and Product of zeros is 4.​

Answer 1

Solution :-

Given,

• one zero of the quadratic polynomial = 3 - √5
• Product of roots or zeroes = 4

✤ Firstly finding other root of the quadratic polynomial .

Let the other root be x

➜ x ( 3 - √5 ) = 4

➜ x = 4/ (3 - √5)

➜ x = 4 ( 3 + √5 )/ ( 3 - √5 ) ( 3 + √5 )

➜ x = 12 + 4√5 / 3² - (√5)²

➜ x = 4(3 + √5) / 9 - 5

➜ x = 4(3 + √5)/4

➜ x = 3 + √5 = Other root of the quadratic polynomial

✤ Now finding the quadratic polynomial .

♦ Quadratic polynomial = x² - (sum of roots)x - product of roots

☞ x² - ( 3 + √5 + 3 - √5 ) x + [ ( 3 + √5 )( 3 - √5 ) ]x

☞ x² - 6x + [ 3² - ( √5 )² ]

☞ x² - 6x + [ 9 - 5 ]

☞ Quadratic polynomial = x² - 6x + 4

Hence,quadratic polynomial is x² - 6x - 4

Answer 2

Use this formula

x = -b ±√b² - 4ac/2a