Question

Question:

Ajay and Vijay solved a quadratic equation. In solving it, Ajay made a mistake in the constant term and got the roots as 6 and 2, while Vijay made a mistake in the coefficient of x only and obtained the roots as –7 and –1. The correct roots of the equations. In answer it is written Ajay sum of the root is correct but if he done mistake in constant term his roots will be in correct.please explain in details

Answer 1

Let the equation be ax²+bx+c.
let the roots of this equation be x1 and x2.
It is known that x1+x2= -b/a.
since ajay made mistake in constant the value of a and b should be equal.
ie., 6+2=8=-b/a -------(1)
And it is also known that x1*x2=c/a
Since vijay made mistake in b his a and c should be correct.
ie., -7*-1=7=c/a --------(2)
​​​​​​Using (1) and (2),
ax²+bx+c=0 becomes x²+b/ax+c/a=0
ie., x²-8x+7=0
Solving we get x1 and x2 as 7 and 1.