Question

The quadratic equation whose roots are 3-√5 and 3+√5 is

Answer 1

Solution is attached below in image

Answer 2

Answer:

The quadratic equation for the roots $3-\sqrt{5}$ and $3+\sqrt{5}$ is $x^{2} -6x+4$.

Step-by-step explanation:

Given:- Roots are $3-\sqrt{5}$ and $3+\sqrt{5}$

To Find:- Quadratic equation for the above roots.

Solution:-

As we know, The expression for a quadratic equation is

= $x^{2} - (sum of roots)x + (product of roots)$

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

= $x^{2} -6x + ((3^{2} )-(\sqrt{5}) ^{2} )$

= $x^{2} -6x+(9-5)$

= $x^{2} -6x+4$

Hence, the quadratic equation for the roots $3-\sqrt{5}$ and $3+\sqrt{5}$ is $x^{2} -6x+4$

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