Same chapter3 marksDifficulty: Medium
Solve x2 − 2x − 8 = 0 and verify the roots by substitution.
Quadratic Equations
3 marksDifficulty: Medium
Show that the equation 3x2 − 2x + 1 = 0 has no real roots.
Original Khojo Papers practice question — not from a past board paper.
Answer
The discriminant is −8, which is negative, so the equation has no real roots.
No citable source has been recorded for this record. Treat it as practice material, not as fact.
Explanation
b2 − 4ac = (−2)2 − 4 × 3 × 1 = 4 − 12 = −8. A negative discriminant means the square root in the formula is not a real number.
Related questions
From the same topic and chapter, at a similar level.
Same chapter3 marksDifficulty: Medium
Find the value of k for which the equation kx2 − 6x + 9 = 0 has equal roots.
Quadratic Equations
Same chapter3 marksDifficulty: Medium
Find the nature of the roots of 4x2 − 12x + 9 = 0 and solve the equation.
Quadratic Equations
Same chapter3 marksDifficulty: Medium
Find the values of k for which x2 + kx + 16 = 0 has equal roots.
Quadratic Equations
Same chapter3 marksDifficulty: Medium
Using the quadratic formula, solve 2x2 + 5x − 3 = 0.
Quadratic Equations
Same chapter2 marksDifficulty: Medium
Assertion: the equation x2 + 4 = 0 has no real roots. Reason: the discriminant of x2 + 4 = 0 is −16. State whether the assertion and the reason are true and whether the reason explains the assertion.
Quadratic Equations