Question

The equation whose roots are 2/3 and 3/2

Answer 1

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  −(  3

​

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  ).

Step-by-step explanation:

Answer 2

Step-by-step explanation:

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