Question

What is the quadratic equation whose roots are2+÷3 and 2-÷3

Answer 1

Step-by-step explanation:

We know that if m and n are the roots of a quadratic equation ax2+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 x2−(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)=22−(3)2=4−3=1(∵a2−b2=(a−b)(a+b))  

Therefore, the required quadratic equation is 

x2−(m+n)x+mn=0

⇒x2−4x+1=0

  

Hence, x2−4x+1=