Question

ramesh and mahesh solve a quadratic equation. ramesh reads its constant term wrongly and finds its roots as 8 and 2 where as mahesh reads the coefficient of x wrongly and finds its roots as-11 and 1 . the correct roots of the equation are

Answer 1

Hi,

11 and -1

Explanation:

The quadratic equation is

`y=ax^2+bx+c\\`

Ramesh:

`y=a(x-8)(x-2)=a(x^2-10x+16)\\c=16a\\`

Mahesh:

`y=a(x+11)(x-1)=a(x^2+10x-11)\\b=10a\\`

The quadratic equation is thus:

`y=a(x^2-10x-11)=a(x^2-11x+x-11)=a(x(x-11)+(x-11))=a(x-11)(x+1)\\\\Correct roots \ are \ 11\ and\ -1\\`