Class 10 • Maths • Chapter 4
QUADRATIC EQUATIONS
True & False Quiz
Discriminant. Roots. Reality.
✓True
✗False
25
Questions
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Ch.4
Chapter
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X
Class
Why True & False for QUADRATIC EQUATIONS?
How this format sharpens your conceptual clarity
🔵 Quadratic Equations are the most-tested equation type in Class X — they appear in geometry, motion, and profit-loss problems.
✅ T/F checks knowledge of the discriminant and nature of roots — exactly two, one, or no real roots.
🎯 D = 0 gives TWO EQUAL real roots, NOT one root — the root is repeated (both roots identical).
📋
Read each statement carefully. Click True or False — instant feedback with explanation appears. Submit anytime; unattempted questions are marked Skipped.
Q 1
The graph of the quadratic equation \(ax^2 + bx + c = 0\) (where \(a ? 0\)) is always a straight line.
Q 2
Every quadratic equation has exactly two real roots.
Q 3
The discriminant of \(x^2 - 4x + 4 = 0\) is zero.
Q 4
If the roots of \(ax^2 + bx + c = 0\) are real and equal, then \(b^2 - 4ac \gt 0\).
Q 5
The quadratic formula is \(x =\frac{ -b \pm \sqrt{(b² - 4ac)}} { 2a}\).
Q 6
For \(2x^2 + 3x - 2 = 0\), the sum of roots is -3/2.
Q 7
The product of roots of \(x^2 - 5x + 6 = 0\) is 6.
Q 8
A quadratic equation can have three distinct real roots.
Q 9
If a and ß are roots of \(x^2 - 7x + 12 = 0\), then a + ß = 7.
Q 10
The equation \(x^2 = 4\) is a quadratic equation.
Q 11
For \(x²^2+ 2x + 5 = 0\), the nature of roots is real and distinct.
Q 12
The roots of \(3x^2 - 6x + 3 = 0\) are real and equal.
Q 13
If product of roots is negative, both roots have opposite signs.
Q 14
The equation \((x - 2)(x + 3) = 0\) has roots 2 and -3.
Q 15
Quadratic equation \(x^2 - 2x - 1 = 0\) has rational roots.
Q 16
Sum of roots of \(5x^2 - 10x + 7 = 0\) is 2.
Q 17
If discriminant is positive, roots are always rational.
Q 18
The quadratic \(x^2 + 4x + 4 = 0\) factors as \((x + 2)^2 = 0\).
Q 19
For equation \(4x^2 - 12x + 9 = 0\), roots are 3/2, 3/2.
Q 20
Nature of roots depends only on coefficient a.
Q 21
Equation \(x^2 - 3x - 10 = 0\) has roots 5 and -2.
Q 22
If both roots are positive, then a and c have opposite signs.
Q 23
Discriminant of \(2x^2 + 5x + 3 = 0\) is 1.
Q 24
Quadratic equation with roots 1, 1 is \(x^2 - 2x + 1 = 0\).
Q 25
The graph of \(y = -x^2 + 1\) opens upwards.
Key Takeaways — QUADRATIC EQUATIONS
Core facts for CBSE Boards & exams
1
Standard form: ax² + bx + c = 0, where a ≠ 0.
2
Discriminant D = b² − 4ac determines nature of roots.
3
D > 0: two distinct real roots; D = 0: two equal real roots; D < 0: no real roots.
4
Quadratic formula: x = (−b ± √D) / 2a.
5
Factorisation method works only when roots are rational.
6
Completing the square works for ALL quadratics regardless of D.