If the coefficient of $x$ in the quadratic equation $x^{2} + b x + c = 0$ was taken as 17 in place of 13, its roots were found to be $- 2$ and $- 15$ . Find the roots of the original equation.

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Solution

Step 1:
Find the value of $c$ :
Put $b = 17$ in given equation:
$x^{2} + 17 x + c = 0$
Since, $- 2$ is the root of this equation, so it must satisfy the equation.
$\begin{array}{rcl} {(- 2)}^{2} + 17 (- 2) + c & = & 0 \\ \Rightarrow & 4 - 34 + c = 0 \\ \Rightarrow & - 30 + c = 0 \\ \Rightarrow & c = 30 \end{array}$
Write the original equation $b = 13$ and $c = 30$ .
$x^{2} + 13 x + 30 = 0 . . . (1)$
Step 2:
Solve the quadratic equation:
Factorize equation (1), and find its roots.
$\begin{array}{rcl} x^{2} + 13 x + 30 & = & 0 \\ \Rightarrow & x^{2} + 10 x + 3 x + 30 = 0 \\ \Rightarrow & x (x + 10) + 3 (x + 10) = 0 \\ \Rightarrow & (x + 3) (x + 10) = 0 \\ \Rightarrow & x + 3 = 0 o r x + 10 = 0 \\ \Rightarrow & x = - 3 o r x = - 10 \end{array}$
Final Answer:
The original roots are $x = - 3 and x = - 10$ .

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If the coefficient of x in the quadratic equation x2+bx+c=0 was taken as 17 in place of 13, its roots were found to be -2 and -15. Find the roots of the original equation.

If the coefficient of $x$ in the quadratic equation $x^{2} + b x + c = 0$ was taken as 17 in place of 13, its roots were found to be $- 2$ and $- 15$ . Find the roots of the original equation.