Question

The coefficients of $x$ in the quadratic equation $x^2+bx+c=0$ was taken as $17$ in place of $13$, it's roots were found to be $-2\text{and}-15.$ The correct roots of the original equation are

• A. $-10,-3$
• B. $-9,-4$
• C. $-8,-5$
• D. $-7,-6$

Answer 1

The correct option is A

$-10,-3$

Explanation for the correct answer:

Finding the real root:

Given equation is $x^2+bx+c=0$ and when $b=17$ the roots are $-2\text{and}-15$

So we can write the quadratic equation as,

$\left(x+2\right)\left(x+15\right)=x^2+17x+30$

On comparing the above equation $x^2+bx+c=0$ we get the value of $c=30$

Now, the quadratic equation can be written with the correct value of $b=13\text{and}c=30$ as

$x^2+13x+30=0$

So, it can be factorized as

$$\begin{gathered} \left(x+3\right)\left(x+10\right)=0 \\ \Rightarrow x=-3\text{and}x=-10 \end{gathered}$$

Hence, option (A) is correct.