Question

find quadratic polynomial each with the given number as a sum of product of its zeros respectively root2 ,1 by 3 ​

Answer 1

Answer:

3x

2

−3

2

x+1

Step-by-step explanation:

We have been given the two roots as \sqrt{2}

2

and \frac{1}{3}

3

1

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} =0x

2

−(

2

)x+

3

1

=0

Taking the LCM:-

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

3

3x

2

−3

2

x+1

=0

Multiply the equation with a constant 'K':-

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

3

3x

2

−3

2

x+1

)=0

Let K = 3

So, the equation becomes:-

3x^2-3\sqrt{2}x+1=03x

2

−3

2

x+1=0

This is the required answer !