Advertisement Remove all ads

For the Equation | X | 2 + | X | − 6 = 0 ,The Sum of the Real Roots is - Mathematics

MCQ

For the equation \[\left| x \right|^2 + \left| x \right| - 6 = 0\] ,the sum of the real roots is

Options

  • 1

  • 0

  • 2

  • none of these

Advertisement Remove all ads

Solution

0

\[\text { Let } p = \left| x \right|\]

\[ \Rightarrow p^2 + p - 6 = 0\]

\[ \Rightarrow p^2 + 3p - 2p - 6 = 0\]

\[ \Rightarrow \left( p + 3 \right)\left( p - 2 \right) = 0\]

\[ \Rightarrow p = - 3, 2\]

\[\text { Also }, \left| x \right| = p\]

\[ \Rightarrow \left| x \right| = 2, or \left| x \right| = - 3\]

\[\text { Modulus can not be negative }, \]

\[ \therefore \left| x \right| = 2\]

\[ \Rightarrow x = \pm 2\]

\[ \Rightarrow x = 2 \text { or } - 2\]

\[\text { Sum of the roots of x is 0 }\]

  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 14 Quadratic Equations
Q 2 | Page 16
Advertisement Remove all ads

Video TutorialsVIEW ALL [1]

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×