CLASS 10 · CHAPTER 04

Quadratic Equations
Practice Questions

20 curated NCERT & Board Exam questions to test your understanding. Click on "Show Solution & Answer" to check step-by-step working.

20Questions

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Q1MCQ1 Mark

Discriminant of 2x² - 4x + 3 = 0 is:

Q2MCQ1 Mark

Roots of x² + 4x + 4 = 0 are:

Q3MCQ1 Mark

If 1/2 is a root of x² + kx - 5/4 = 0, value of k is:

Q4MCQ1 Mark

Roots of 2x² - x - 6 = 0 are:

Q5Assertion-Reason1 Mark

Assertion (A): Equation x² + 3x + 4 = 0 has no real roots. Reason (R): A quadratic equation has no real roots if D < 0.

Q6Assertion-Reason1 Mark

Assertion (A): Roots of x² - 5x + 6 = 0 are 2 and 3. Reason (R): Sum of roots = -b/a = 5, Product of roots = c/a = 6.

Q7Short Answer2 Marks

Find roots of 3x² - 2√6 x + 2 = 0.

Q8Short Answer2 Marks

Find k if 2x² + kx + 3 = 0 has equal roots.

Q9Short Answer2 Marks

Find two numbers whose sum is 27 and product is 182.

Q10Short Answer2 Marks

Solve x² - 3x - 10 = 0 using quadratic formula.

Q11Short Answer2 Marks

Find discriminant of 3x² - 2x + 1/3 = 0 and state nature of roots.

Q12Long Answer3 Marks

Altitude of right triangle is 7cm less than base. Hypotenuse is 13cm. Find sides.

Q13Long Answer3 Marks

Solve for x: 1/(x+4) - 1/(x-7) = 11/30 (x ≠ -4, 7).

Q14Long Answer3 Marks

Two taps fill tank in 9 3/8 hrs. Larger tap takes 10 hrs less than smaller. Find individual times.

Q15Long Answer3 Marks

Find k for which (k+4)x² + (k+1)x + 1 = 0 has equal roots.

Q16Case Study4 Marks

Case Study Scenario: A rectangular park of length l and breadth b has area 300 m² and perimeter 70 m. Question: Find length and breadth of rectangular park.

Q17Case Study4 Marks

Case Study Scenario: Speed of motor boat in still water is 15 km/h. It goes 30 km downstream and returns in 4 hrs 30 mins. Question: Find speed of stream.

Q18PYQ5 Marks

Express train takes 1 hr less than passenger train for 132 km. Express speed is 11 km/h more. Find speeds.

Q19PYQ5 Marks

Solve for x: 4x² - 4ax + (a² - b²) = 0.

Q20PYQ5 Marks

Quadratic Equations Practice Questions