Question

A and B solved a quadratic equation. In solving it, A made a mistake in the constant term and obtained the roots as $5,-3$, while B made a mistake in the coefficient of x and obtained the roots as $1,-3$. The correct roots of the equation are

• A. $1,3$
• B. $-1,3$
• C. $-1,-3$
• D. $1,-1$

Answer 1

The correct option is B $-1,3$

A's quadratic equations was

$x^2-(5-3)x+5\times (-3)=0$

$x^2-2x-15=0$

B's quadratic equations was

$x^2-(1-3)x+1\times (-3)=0$

$x^2+2x-3=0$

Since A made a mistake in the constant term and B made a mistake in coefficient of x

therefore the correct equation was

$x^2-2x-3=0$

$⟹(x-3)(x+1)=0$

$⟹x=3,-1$

∴ Roots of the correct equation are 3,−1.