Question

Write a quadratic polynomial sum of whose zeros is 2root3 and their product is 2. Mark Questions:

don't give wrong answer
give answer with explanation​

Answer 1

Given : Write a quadratic polynomial sum of whose zeros is 2√3 and their product is 2.

Need to Find : We have to write a quadratic polynomial whose sum of zeros & product of zeros are given .

According to the Question

• Sum of zeros = 2√3
• Product of zeros = 2

Let the zeros of polynomial be

$\sf \alpha \: and \: \beta$

$\implies \sf \: \alpha \: + \beta \: = 2 \sqrt{3} \\ \\ \\ \implies \sf \: \alpha \beta \: = 2$

Let the ploynomial be p(x)

$\implies \sf \: p(x) \: = {x}^{2} \: - (sum \: of \: zeros)x \: \: + product \: of \: zeros$

$\implies \sf \: p(x) \: = {x}^{2} - (2 \sqrt{3})x \: + 2 \\ \\ \implies \sf \: p(x) \: = {x}^{2} - 2 \sqrt{3} \: x \: + 2$

Answer 2

INFORMATION PROVIDED :-

• quadratic polynomial sum of whose zeros is 2root3 and their product is 2

TO CALCULATE :-

• what is the product is 2 = ?

CONCEPT USED :-

• formula to find root x^2 - (sum of zeroes ) + (product of zeroes)

UNDERSTANDING CONCEPT :-

• Use the direct formula to get a quadratic equation when its sum of the roots and product of the roots are given, that is x^2 - (sum of zeroes ) + (product of zeroes)

SOLUTION :-

Given :-

It is given that the sum of zeros is

2√3 and the product of zeros is 2

Assume the polynomial to be ax² + bx + c

Now, the sum,

(-b/a) = 2 √3

Now, the product,

(c/a) = 2

Consider the equation (i), (ii), place the values of

(-b/a) , c/a , in the polynomial and equate it to zero,

ax² - a (-b/a) x + a (c/a) = 0

a { x² - (-b/a) x + a (c/a) } = 0

x² - 2√3x + 2 = 0 (taking 'a' common as a = 0)

Thus, the quadratic polynomial is

x² - 2√3x + 2

NOTE :-

• In case if you don't remember the direct formula you can assume the two roots and make two equations using the information given in the question, solve to find those two roots and write the quadratic equation as x^2 - (sum of zeroes ) + (product of zeroes)