Question

write a quadratic polynomial sum of whose zeros is 2 under root 3 and their product is 20

Answer 1

Step-by-step explanation:

Sum of zeros = 2√3

product of zeros = 20

Quadratic equation,

x² + (sum of zeros)x + product of zeros

= x² + 2√3x + 20

Answer 2

Answer:-

Given:-

• The sum of the two zeroes of a polynomial is 2√3

• The product of the zeroes is 20 .

To Find:-

• The quadratic polynomial

Solution:-

The sum of the zeroes of a polynomial is =

( α + β )

= $\dfrac{-b}{a}$

= $\dfrac{Coefficient \: of \: x}{Coefficient \: Of \: x²}$

= 2√3

The product of the zeroes of a polunomial

= αβ

= $\dfrac{C}{a}$

= $\dfrac{Constant \: Term\: x}{Coefficient \: Of \: x²}$

= 20

The required quadratic polynomial becomes,

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

= x² - ( 2√3) x + 20

= x² - 2√3x + 20

Therefore , the polynomial is x² - 2√3x + 20 .