Question

Write down the quadratic equation whose roots are 3+√2 and 3-√2.
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Answer 1

Answer:

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Answer 2

Answer:

We know that if m and n are the roots of a quadratic equation ax

2

+bx+c=0, then the sum of the roots is (m+n) and the product of the roots is (mn). And then the quadratic equation becomes x

2

−(m+n)x+mn=0

Here, it is given that the roots of the quadratic equation are m=(2+

3

) and n=(2−

3

), therefore,

The sum of the roots is:

m+n=2+

3

+2−

3

=2+2=4

And the product of the roots is:

mn=(2+

3

)×(2−

3

)=2

2

−(

3

)

2

=4−3=1(∵a

2

−b

2

=(a−b)(a+b))

Therefore, the required quadratic equation is

x

2

−(m+n)x+mn=0

⇒x

2

−4x+1=0

Hence, x

2

−4x+1=0 is the quadratic equation whose roots are (2+

3

) and (2−

3

).