Question

Find the quadratic pokynomial whose zerosare 3+root 5 and 3-root 5

Answer 1

Answer:

x² + 6x + 4

Step-by-step explanation:

Let the zeroes of the required polynomial be α and β.

A.T.Q

α = 3 + √5 and β = 3 - √5

Now,

Product of zeroes = αβ

= (3 + √5)(3 - √5)

= (3)² - (√5)²

= 9 - 5 = 4

Sum of zeroes = α + β

= 3 + √5 + 3 - √5

= 6

The required polynomial is :

→ p(x) = k[x² + (α + β)x + αβ]

→ p(x) = k[x² + (6)x + 4]

→ p(x) = k[x² + 6x + 4]

Putting k = 1, we get

→ p(x) = x² + 6x + 4