Q1
Not Answered
NATIVE
Q1. Find roots of x^2 + 15x + 54 = 0
x^2 + 15x + 54 = (x+6)(x+9). Roots are -6 and -9.
Home / General Aptitude / Quadratic problems
General Aptitude
Quadratic problems
Practice roots, factorization, and quadratic relationship questions commonly asked in aptitude tests.
About Quadratic problems
Quadratic equations are a high-weightage topic in quantitative aptitude, appearing in placement tests, banking exams, and competitive entrance exams. A quadratic equation is of the form ax² + bx + c = 0, where a ≠ 0. Key concepts tested include: finding roots using factorization or the quadratic formula, sum and product of roots (sum = -b/a, product = c/a), forming an equation given its roots, nature of roots (real vs imaginary, equal vs distinct), and relationship between coefficients and roots. Common exam questions also involve comparing roots of two different quadratics and word problems that translate into quadratic form. Below are solved quadratic equation questions with comprehensive explanations.
Key Takeaways
- Sum of roots = -b/a. Product of roots = c/a. For x² - 5x + 6 = 0, roots sum to 5.
- Discriminant D = b² - 4ac. D > 0: real distinct roots. D = 0: equal roots. D < 0: complex roots.
- To form equation from roots p, q: x² - (p+q)x + pq = 0.
Frequently Asked Questions
How to find roots using the quadratic formula?
For ax² + bx + c = 0: x = [-b ± √(b² - 4ac)] / 2a. The discriminant (b² - 4ac) tells you the nature of roots: positive = two real distinct roots, zero = one real repeated root, negative = no real roots (complex).
What is the relationship between roots and coefficients?
Sum of roots = -b/a. Product of roots = c/a. You can find these without solving the equation. If roots are p and q: equation is x² - (p+q)x + pq = 0. Use this for 'form equation from roots' problems.
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Q2
Not Answered
NATIVE
Q2. Find roots of x^2 + 7x + 10 = 0
x^2 + 7x + 10 = (x+5)(x+2). Roots are -5 and -2.
Q3
Not Answered
NATIVE
Q3. For x^2 - 4x + 3 = 0, what is the sum of roots?
For ax^2+bx+c=0, sum = -b/a. Here sum = 4.
Q4
Not Answered
NATIVE
Q4. Find roots of x^2 + 10x + 25 = 0
x^2 + 10x + 25 = (x+5)(x+5). Roots are -5 and -5.
Q5
Not Answered
NATIVE
Q5. Find roots of x^2 + 9x + 14 = 0
x^2 + 9x + 14 = (x+2)(x+7). Roots are -2 and -7.
Q6
Not Answered
NATIVE
Q6. Find roots of x^2 + 10x + 24 = 0
x^2 + 10x + 24 = (x+4)(x+6). Roots are -4 and -6.
Q7
Not Answered
NATIVE
Q7. For x^2 - 7x + 6 = 0, what is the product of roots?
Product of roots = c/a = 6/1 = 6.
Q8
Not Answered
NATIVE
Q8. Find roots of x^2 + 17x + 72 = 0
x^2 + 17x + 72 = (x+9)(x+8). Roots are -9 and -8.
Q9
Not Answered
NATIVE
Q9. For x^2 - 18x + 80 = 0, what is the sum of roots?
For ax^2+bx+c=0, sum = -b/a. Here sum = 18.
Q10
Not Answered
NATIVE
Q10. For x^2 - 17x + 60 = 0, what is the sum of roots?
For ax^2+bx+c=0, sum = -b/a. Here sum = 17.
Q11
Not Answered
NATIVE
Q11. For x^2 - 6x + 8 = 0, what is the product of roots?
Product of roots = c/a = 8/1 = 8.
Q12
Not Answered
NATIVE
Q12. For x^2 - 18x + 81 = 0, what is the product of roots?
Product of roots = c/a = 81/1 = 81.
Q13
Not Answered
NATIVE
Q13. For x^2 - 14x + 48 = 0, what is the sum of roots?
For ax^2+bx+c=0, sum = -b/a. Here sum = 14.
Q14
Not Answered
NATIVE
Q14. For x^2 - 13x + 30 = 0, what is the product of roots?
Product of roots = c/a = 30/1 = 30.
Q15
Not Answered
NATIVE
Q15. For x^2 - 11x + 24 = 0, what is the sum of roots?
For ax^2+bx+c=0, sum = -b/a. Here sum = 11.
Q16
Not Answered
NATIVE
Q16. For x^2 - 8x + 7 = 0, what is the product of roots?
Product of roots = c/a = 7/1 = 7.
Q17
Not Answered
NATIVE
Q17. Find roots of x^2 + 8x + 12 = 0
x^2 + 8x + 12 = (x+6)(x+2). Roots are -6 and -2.
Q18
Not Answered
NATIVE
Q18. For x^2 - 6x + 8 = 0, what is the sum of roots?
For ax^2+bx+c=0, sum = -b/a. Here sum = 6.
Q19
Not Answered
NATIVE
Q19. For x^2 - 8x + 12 = 0, what is the product of roots?
Product of roots = c/a = 12/1 = 12.
Q20
Not Answered
NATIVE
Q20. For x^2 - 16x + 55 = 0, what is the sum of roots?
For ax^2+bx+c=0, sum = -b/a. Here sum = 16.
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Quadratic problems Formula, shortcuts & preparation guide
Master quadratic problems with regular practice. Key topics include percentage calculations, profit/loss, ratio, and time-work problems. Use shortcut methods for quick calculations and practice 15-20 questions daily to build speed and accuracy. This topic frequently appears in placement aptitude rounds.
Key formulas
- Regular practice improves accuracy
Quadratic problems Practice Questions with Answers
Build speed and accuracy with curated quadratic problems practice. Each quiz includes solved explanations, timed mode, and instant correctness feedback.
How to prepare effectively for this topic?
Practice short timed sets daily, review every explanation, and track recurring mistakes for weekly revision.
Are these questions useful for placements and competitive exams?
Yes. The format mirrors common screening rounds with option-based answers and explanation-driven learning.