Question

From the quadratic equation whose roots are 2+√3, 2-3
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Answer 1

Answer:

x^2−4x+1=0

Step-by-step explanation:

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+root 3) and n=(2−root 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)=22−(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, x2−4x+1=0 is the quadratic equation whose roots are (2+ root 3) and (2−root 3).