If the equations ${x^2} + ax + bc = 0\,and\,{x^2} + bx + ca = 0$ have a common root and if a, b and c are non-zero distinct real numbers, then their roots satisfy the equation: A. ${x^2} + x + abc = 0\,\,$ B. ${x^2} - \left( {a + b} \right)x + ab = 0\,\,$ C. ${x^2} + \left( {a + b} \right)x + ab = 0\,\,$ D. ${x^2} + x + ab = 0\,\,$ E. ${x^2} + abx + abc = 0\,\,$
Answer
Verified
Hint: We have been given with two equations, to find a common root we will solve both the equations.
We will subtract the second equation from the first one, $\left( {a - b} \right)x + c\left( {b - a} \right) = 0$ $ \Rightarrow \left( {a - b} \right)\left( {x - c} \right) = 0$ is the common root. Thus, the roots of ${x^2} + ax + bc = 0$ are b and c and that of ${x^2} + bx + ca = 0$ are c and a. If roots are b and a, then the equation will be, ${x^2} - \left( {a + b} \right)x + ab = 0\,$ Answer is option B
Note: In this question, we solved the equations first and then found the common root and then form the equation using the roots.
×
Sorry!, This page is not available for now to bookmark.