Question

Find A Quadratic Polynomial With Zeroes Roote3+Roote2 And Roote3-Roote2

Answer 1

Step-by-step explanation:

▶we have given Two zeros of the quadratic polynomial

let us consider,

α = √3 + √2

β = √3 - √2

▶we know the formula to making a quadratic equation,

x² - (α + β)x + (α.β)

→ x² - ((√3+√2)+(√3 -√2))x +((√3+√2)x((√3 - √2))

→ x² - (√3 + √2 +√3 -√2)+((√3)²-(√2)²)

→ x² - (2√3)x + (3 - 2)

→ x² - (2√3)x + 1

The required quadratic equation is x² - (2√3)x + 1 whose zeroes are

√3 + √2 and √3 - √2

Answer 2

Answer:

x² - 2√3x + 1

Step-by-step explanation:

given that,

zeros of a quadratic equation

= √3 + √2

and √3 - √2

and we know that,

when the zeros of the quadratic equation is given then

quadratic equation will be

x² - sum of zeros × x + product of zeros

here,

sum of zeros = √3 + √2 + √3 - √2

= 2√3

product of zeros = (√3 + √2) (√3 - √2)

= 3 - 2

= 1

so,

now we have,

product of zeros = 2√3

sum of zeros = 1

so,

quadratic equation

= x² - 2√3x + 1