Question

The coefficient of x in the equation $a{x}^2+bx+c=0$ was wrongly taken as 17 instead of 30 and its roots came out to be -2, -15. The actual roots were:

• A. -2,-15
  
• B. -3,-10
• C. -5,-6
  
• D. None of these

Answer 1

The correct option is D None of these

The sum of the roots = -b/a
The product of the roots = c/ a
If we know the sum and the product of the roots, the quadratic equation is $x^2-\left(b/a\right)x+\left(c/a\right)=0$
In the both cases, the product of roots is same (i.e. product of the roots $c=(-15)\times (-2)=30$)
So, the wrong equation = $x^2+17x+30=0$
The actual equation = $x^2+30x+30=0$
Roots of a quadratic equation $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$
By using the above equation, actual roots = $x=\frac{-30\pm \sqrt{{30}^2-4\times 30}}{2}$
$x=\frac{-30\pm \sqrt{780}}{2}$
$x=-15\pm \sqrt{195}$