Question

√2,1/3 find the quadratic polynomial with the given numbers as the sum and product of its zeroes respectively
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Answer 1

this is polynomial of given product and sum

Answer 2

Answer:

$3x^2-3\sqrt{2}x+1$

Step-by-step explanation:

We have been given the two roots as $\sqrt{2}$ and $\frac{1}{3}$

We can find easily find the required quadratic equation with the given sum and product of the roots.

Any equation is in the form:-

x² - Sx + P = 0

Here,

S = Sum of Roots

P = Product of Roots

Substitute the values:-

$x^{2}-(\sqrt{2})x+\dfrac{1}{3} =0$

Taking the LCM:-

$\dfrac{3x^{2}-3\sqrt{2}x+1}{3}=0$

Multiply the equation with a constant 'K':-

$K\left(\dfrac{3x^{2}-3\sqrt{2}x+1}{3}\right)=0$

Let K = 3

So, the equation becomes:-

$3x^2-3\sqrt{2}x+1=0$

This is the required answer !