Question

find the quadrtic polynomial whose zeroes are 2+√3 and 2-√3​

Answer 1

ANSWER:

• Quadratic polynomial = x²-4x+1

GIVEN:

• First zero (α) = 2+√3
• Second zero (β) = 2-√3

TO FIND :

• Quadrtic polynomial whose zeroes are 2+√3 and 2-√3.

SOLUTION:

Standard form of Quadratic polynomial when Zeros are given:

= x²-(α+β)x+αβ. ..,..(i)

Finding sum of zeros: (α+β)

=> α = 2+√3

=> β = 2-√3

=> α+β = 2+√3+2-√3

=> α+β = 4

Finding product of zeros : (αβ)

=> α = 2+√3

=> β = 2-√3

=> αβ = (2+√3)(2-√3)

=> αβ = 4-3

=> αβ = 1

Putting these values in eq(i) we get:

= x²-4x+1

Quadratic polynomial = x²-4x+1

NOTE:

Some important formulas:

(a+b)(a-b) = a²-b²

(a+b)³ = a³+b³+3ab(a+b)

(a-b)³ = a³-b³-3ab(a-b)

Answer 2

Answer:

x² - 4x + 1

Step-by-step explanation:

(x - (2+√3))(x - (2 - √3)) =

x² - 2x - √3x - 2x + 4 + 2√3 + √3x - 2√3 - 3 =

x² - 4x + 1