Question

If two persons $A$ and $B$ solve the equation, $x^2+ax+b=0$, while solving, $A$ commits a mistake the coefficient of $x$ was taken as in $15$place of $-9$and finds the roots as $-7$and $-2$ Then, the equation is.

• A. $x^2+9x+14=0$
• B. $x^2–9x+14=0$
• C. $x^2+9x–14=0$
• D. $x^2–9x–14=0$
• E. None of these

Answer 1

The correct option is B

$x^2–9x+14=0$

Explanation for the correct answer:

To find the required equation:

Given,

The incorrect equation is $x^2–15x+b=0.$

It is given that$–7,–2$are the roots of the incorrect equation is

We know that product of roots is $\frac{b}{1}$ that is constant divided by the coefficient of $x^2$.

So,

$\begin{array}{rcl}(-7)(-2)& =& b\\ b& =& 14\end{array}$

Hence, the correct option is B.