Question

form a quadratic polynomial whose zeroes are
$3 + \sqrt{15}$
and
$3 - \sqrt{15}$
​

Answer 1

Sum of zeroes = 3 + √15 + 3 - √15 = 6

Product of zeroes = (3 + √15) (3 - √15) = 9 - 15 = (-6)

Polynomial = x^2 - (sum)x + product

Answer: x^2 - 6x - 6

Answer 2

Answer: x² - 6x - 6 = 0

Step by step explanation:

Let α & β be the zeroes of the polynomial.

α = 3 + √15 and β = 3 - √15

The formula to get the equation:

x² - ( sum of roots )x + (product of roots) = 0

Sum of roots = α + β and product = αβ

Here,

α + β = (3 + √15) + (3 - √15)

= 6

and αβ = (3 + √15) (3 - √15)

= 9 - 15 = -6

= x² - 6x -6 = 0

.°. x² - 6x -6 = 0

Thus, the quadratic polynomial formed is: x² - 6x - 6 = 0