Welcome to AssamSchool. This article contains 30 Extra Questions from Quadratic Equations from Class 10 Mathematics Chapter 4. These Quadratic Equations Class 10 Extra Questions are helpful to test your understanding and knowledge of the chapter. These additional questions will not only help you to excel in the chapter but also give you a strong foundation in Mathematics.
We have also provided step-by-step answers to the questions for reference. So, let’s start…
30 Quadratic Equations Class 10 Extra Questions
1. Check whether the equation \( (3x – 1)^2 = 5(x + 2) \) is quadratic.
2. Represent the situation mathematically: The product of two consecutive odd integers is 143.
3. Solve by factorization: \( x^2 + 8x + 15 = 0 \).
4. Find the roots of \( 4x^2 – 12x + 9 = 0 \) using the quadratic formula.
5. Determine the nature of the roots of \( 3x^2 – 7x + 2 = 0 \) without solving.
6. A rectangular field has an area of \(120 \,m²\). If its length is \(2\, m\) more than its breadth, find its dimensions.
7. For what value of \( k \) does \( kx^2 + 4x + 1 = 0 \) have equal roots?
8. Solve \( 2x^2 – 5x – 3 = 0 \) by factorization.
9. Verify if \( x = -2 \) is a root of \( 2x^2 + 3x – 2 = 0 \).
10. The sum of a number and its reciprocal is \( \frac{10}{3} \). Find the number.
11. Find the discriminant of \( 5x^2 – 6x + 2 = 0 \) and interpret its nature.
12. A train travels 300 km at a uniform speed. If the speed were 5 km/h less, it would take 2 hours more. Find the original speed.
13. Solve \( \sqrt{2}x^2 + 7x + 5\sqrt{2} = 0 \).
14. Two numbers differ by 3, and their product is 108. Find the numbers.
15. Check if the equation \( x^3 – 3x^2 + 2x = 0 \) is quadratic. Justify.
16. The hypotenuse of a right-angled triangle is 15 cm. If one leg is 3 cm shorter than the other, find the legs.
17. Determine if \( x = \frac{1}{2} \) is a solution to \( 4x^2 – 8x + 3 = 0 \).
18. A quadratic equation has roots \( 2 \) and \( -3 \). Write the equation.
19. Solve \( 3x^2 – 2x – 1 = 0 \) using the quadratic formula.
20. A garden is 2 meters longer than wide. If its area is 48 m², find its dimensions.
21. Find \( k \) if \( x^2 + kx + 9 = 0 \) has real and equal roots.
22. The sum of the ages of a father and son is 45. Five years ago, the father was four times as old. Find their current ages.
23. Solve \( x^2 – 4x + 4 = 0 \) and state the nature of the roots.
24. A number exceeds its square by 30. Find the number.
25. Determine if \( 2x^2 + 3x + \frac{9}{8} = 0 \) has real roots.
26. The perimeter of a rectangle is 40 m, and its area is 96 m². Find its length and breadth.
27. Solve \( 10x^2 – 13x – 3 = 0 \) by factorization.
28. Find the roots of \( x^2 – 2\sqrt{5}x + 3 = 0 \).
29. A natural number is 12 more than its reciprocal. Find the number.
30. Is the equation \( (x + 4)(x – 3) = x^2 – 7x + 10 \) quadratic? Simplify and check.
Answers
- Solution:
Expand \( (3x – 1)^2 = 9x^2 – 6x + 1 \)
Equation becomes \( 9x^2 – 6x + 1 = 5x + 10 \)
simplify to \( 9x^2 – 11x – 9 = 0 \)
Yes, quadratic. - Solution:
Let numbers be \( x \) and \( x + 2 \)
\( x(x + 2) = 143 \Rightarrow x^2 + 2x – 143 = 0 \) - Solution:
\( x^2 + 8x + 15 = (x + 3)(x + 5) = 0 \)
Roots: \( x = -3, -5 \) - Solution:
\( x = \frac{12 \pm \sqrt{144 – 144}}{8} = \frac{12}{8} = \frac{3}{2} \)
Repeated root: \( x = \frac{3}{2} \) - Solution:
Discriminant \( D = (-7)^2 – 4(3)(2) = 25 > 0 \)
Two distinct real roots. - Solution:
Let breadth = \( x \), length = \( x + 2 \)
\( x(x + 2) = 120 \Rightarrow x^2 + 2x – 120 = 0 \)
Solve: \( x = 10 \)
Dimensions: 10 m × 12 m. - Solution:
For equal roots: \( 16 – 4k = 0 \Rightarrow k = 4 \) - Solution:
\( 2x^2 – 5x – 3 = (2x + 1)(x – 3) = 0 \)
Roots: \( x = -\frac{1}{2}, 3 \) - Solution:
Substitute \( x = -2 \): \( 2(4) + 3(-2) – 2 = 8 – 6 – 2 = 0 \)
Yes, valid root. - Solution:
Let number = \( x \)
\( x + \frac{1}{x} = \frac{10}{3} \Rightarrow 3x^2 – 10x + 3 = 0 \)
Roots: \( x = 3, \frac{1}{3} \) - Solution:
Discriminant \( D = 36 – 40 = -4 \)
No real roots. - Solution:
Let speed = \( x\)
\( \frac{300}{x – 5} – \frac{300}{x} = 2 \Rightarrow x^2 – 5x – 750 = 0 \)
Solve: \( x = 30 \) km/h. - Solution:
\( \sqrt{2}x^2 + 7x + 5\sqrt{2} = (\sqrt{2}x + 5)(x + \sqrt{2}) = 0 \)
Roots: \( x = -\frac{5}{\sqrt{2}}, -\sqrt{2} \) - Solution:
Let numbers be \( x \) and \( x + 3 \)
\( x(x + 3) = 108 \Rightarrow x^2 + 3x – 108 = 0 \)
Solve: \( x = 9\)
Numbers: 9 and 12. - Solution:
Simplify: \( x(x^2 – 3x + 2) = 0 \)
Not quadratic \(degree 3\). - Solution:
Let legs = \( x \), \( x + 3 \)
\( x^2 + (x + 3)^2 = 225 \Rightarrow 2x^2 + 6x – 216 = 0 \)
Solve: \( x = 9 \).
Legs: 9 cm, 12 cm. - Solution:
Substitute \( x = \frac{1}{2} \): \( 4(\frac{1}{4}) – 8(\frac{1}{2}) + 3 = 1 – 4 + 3 = 0 \)
Valid. - Solution:
Equation: \( (x – 2)(x + 3) = x^2 + x – 6 = 0 \) - Solution:
\( x = \frac{2 \pm \sqrt{4 + 12}}{6} = \frac{2 \pm 4}{6} \Rightarrow x = 1, -\frac{1}{3} \) - Solution:
Let breadth = \( x \), length = \( x + 2 \)
\( x(x + 2) = 48 \Rightarrow x = 6 \)
Dimensions: 6 m × 8 m. - Solution:
Discriminant \( k^2 – 36 = 0 \Rightarrow k = \pm 6 \) - Solution:
Let son’s age = \( x \), father’s = \( 45 – x \)
\( (45 – x – 5) = 4(x – 5) \Rightarrow x = 10 \)
Ages: 10 and 35. - Solution:
\( (x – 2)^2 = 0 \Rightarrow x = 2 \)
Repeated roots. - Solution:
Let number = \( x \)
\( x – x^2 = 30 \Rightarrow x^2 – x + 30 = 0 \)
Discriminant \( D = 1 – 120 = -119 \)
No real solution. - Solution:
Discriminant \( D = 9 – 4(2)(\frac{9}{8}) = 9 – 9 = 0 \)
Equal real roots. - Solution:
Let length = \( l \), breadth = \( 20 – l \)
\( l(20 – l) = 96 \Rightarrow l^2 – 20l + 96 = 0 \)
Solve: \( l = 12 \)
Dimensions: 12 m × 8 m. - Solution:
\( 10x^2 – 13x – 3 = (5x + 1)(2x – 3) = 0 \)
Roots: \( x = -\frac{1}{5}, \frac{3}{2} \) - Solution:
\( x = \frac{2\sqrt{5} \pm \sqrt{20 – 12}}{2} = \sqrt{5} \pm \sqrt{2} \) - Solution:
Let number = \( x \)
\( x – \frac{1}{x} = 12 \Rightarrow x^2 – 12x – 1 = 0 \)
Roots: \( x = 6 \pm \sqrt{37} \) - Solution:
Expand: \( x^2 + x – 12 = x^2 – 7x + 10 \)
Simplify: \( 8x – 22 = 0 \)
Not quadratic (linear).
The Bottom Line
I hope these extra questions have helped you a lot. Remember, math is all about practice, so don’t hesitate to revisit these questions and explore more on your own. If you found this post, Quadratic Equations Class 10 Extra Questions, helpful, feel free to share it with your friends or classmates who might benefit from it.
If you find any mistakes in the above questions and answers or have any other issues regarding the content of this website, feel free to contact us through the Contact Us section.
You can also check the related MCQs for this chapter here: MCQ on Quadratic Equations
Thank you for visiting our blog. Have a great day.
Abdur Rohman is an Electrical Engineer from Charaideo, Assam, who wears multiple hats as a part-time teacher, blogger, entrepreneur, and digital marketer. Passionate about education, he founded The Assam School blog to provide free, comprehensive textbook solutions, MCQs (Multiple Choice Questions), and other academic content for students from Class V to XII.