Published by:
CGP EDU Academic Team
Published on: August 14, 2026
If
, then prove that the roots of the equation
are always real and cannot have roots if
.
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
Sol. Simplifying

Let





(assuming
)
If two roots are real, then the polynomial of degree three has the third root which must be real.
──────────────────────────────────────────────────────────────────────────────────────────
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems
If is a root of the equation (where and ), then find the ordered pair ( ).
If the roots of the equation are real and unequal, then prove that the roots of will be imaginary.
For what values of k the expression will be a perfect square of a linear polynomial.
Show that if roots of equation are equal, then either or
If the roots of the equation are equal in magnitude but opposite in sign, then show that and that…
(i) If is a root of (where and ), then find roots of equation. (ii) , is a root of (where a…