Question

Find the quadratic equation, if one of the roots is √5 -√3
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Answer 1

Answer:

The quadratic equation is x²+2(√3+√5)x+ (8-2√15)

Step-by-step explanation:

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Answer 2

Given :

The roots of the equation is $\sqrt{5}$ and $-\sqrt{3}$.

To find :

The quadratic equation.

Step-by-step explanation:

• The quadratic equation can be found by following these steps.
• It is given that the roots are $\sqrt{5}$ and $-\sqrt{3}$.
• The value of $x$ is equated to the roots of the equation
• An quadratic equation when the roots are given can be written as

      $x=\sqrt{5}$ and $x=-\sqrt{3}$

• Bring the roots to the other side of the equation

      $x-\sqrt{5} =0$

• The other term will be

       $x+\sqrt{3} =0$

• Multiply both the terms

       $(x-\sqrt{5} )(x+\sqrt{3} ) =0$

• The formula used is

      $(x-a)(x-b)=x^{2} -xb-xa+ab$

• Substitute the values in the formula

       $(x-\sqrt{5} )(x+\sqrt{3} )=x^{2} +\sqrt{3}x-\sqrt{5} x-\sqrt{15}$

• The quadratic equation is

       $x^{2} +\sqrt{3}x-\sqrt{5} x-\sqrt{15}=0$

Final answer :

The quadratic equation when the roots are $\sqrt{5}$ and $-\sqrt{3}$ is $x^{2} +\sqrt{3}x-\sqrt{5} x-\sqrt{15}=0$.