Question

Sum of zeroes = ✓2
Product of zeroes =1/3
Find the polynomial

Answer 1

Hey mate,

Your answer is

3x^2 - 3×root (2)×x + 1

hope this helps you out!

Answer 2

Error:

→ It will be find the quadratic polynomial .


Answer :

→ 3x² - 3√2x + 1 = 0 .


Step - by - step explanation :

Let alpha and beta are the two zeros of quadratic polynomial .


▶ Given :-

→ Sum of zeros = √2.

$( \alpha + \beta = \sqrt{2} ).$

→ Product of zeros = 1/3 .

$( \alpha \times \beta = \frac{1}{3} ).$

▶ To find :-

→ The quadratic polynomial .


▶ Solution :-

We know that :-

→ A quadratic polynomial whose zeros are alpha and beta is given by .

$\sf \because p(x) = ( {x}^{2} - ( \alpha + \beta )x + \alpha \beta ).$

[ The required polynomial { p(x) } = x² - ( sum of zeros )x + product of zeros . ]


$\sf \implies {x}^{2} - ( \sqrt{2} )x + \frac{1}{3} = 0 . \\ \\ \sf \implies {x}^{2} - \sqrt{2} x + \frac{1}{3} = 0. \\ \\ \sf \implies \frac{3 {x}^{2} - 3 \sqrt{2} x + 1}{3} = 0. \\ \\ \boxed{ \green{ \sf \implies3 {x}^{2} - 3 \sqrt{2} x + 1 = 0.}}$


✔✔ Hence, it is solved ✅✅.


THANKS