Quadratic Equations

What you'll learn

Learn what quadratic equations are and how to solve them by factorisation, completing the square and the quadratic formula, plus using the discriminant to judge the nature of roots — with a worked example and a self-check quiz.

This chapter has

Quadratic Equations — solved practice questions

8 Class 10 Mathematics questions with step-by-step solutions. Attempt each, then reveal the answer.

1. Q1easy

   Which of the following is a quadratic equation?

   • Ax + 5 = 0
   • Bx² + 5x + 6 = 0
   • Cx³ + 1 = 0
   • D1/x = 2
   Show answer & solution

   Correct answer: (B) x² + 5x + 6 = 0

   A quadratic equation has degree 2. x² + 5x + 6 = 0 is degree 2; the others are not.

2. Q2easy

   The standard form of a quadratic equation is:

   • Aax² + bx + c = 0
   • Bax + b = 0
   • Cax³ + bx² + c = 0
   • Da/x + b = 0
   Show answer & solution

   Correct answer: (A) ax² + bx + c = 0

   ax² + bx + c = 0 where a ≠ 0 is the standard form.

3. Q3medium

   What are the roots of x² − 5x + 6 = 0?

   • A1 and 6
   • B2 and 3
   • C−2 and −3
   • D1 and 5
   Show answer & solution

   Correct answer: (B) 2 and 3

   Factorise: (x − 2)(x − 3) = 0 → x = 2 or x = 3.

4. Q4medium

   The discriminant of ax² + bx + c = 0 is:

   • Ab² + 4ac
   • B4ac − b²
   • Cb² − 4ac
   • Db + 4ac
   Show answer & solution

   Correct answer: (C) b² − 4ac

   D = b² − 4ac. It determines the nature of roots.

5. Q5medium

   If discriminant D > 0, the roots are:

   • Atwo distinct real roots
   • Btwo equal real roots
   • Cno real roots
   • Dcomplex roots
   Show answer & solution

   Correct answer: (A) two distinct real roots

   D > 0 means two distinct real roots.

6. Q6medium

   If discriminant D = 0, the roots are:

   • Atwo distinct real roots
   • Btwo equal real roots
   • Cno real roots
   • Dirrational
   Show answer & solution

   Correct answer: (B) two equal real roots

   D = 0 means two equal (repeated) real roots.

7. Q7medium

   If discriminant D < 0, the roots are:

   • Aequal
   • Bdistinct real
   • Cno real roots
   • Drational
   Show answer & solution

   Correct answer: (C) no real roots

   D < 0 means no real roots — the roots are imaginary.

8. Q8easy

   Find the roots of x² − 4 = 0.

   • A2 and −2
   • B4 and −4
   • C2 and 4
   • D1 and −1
   Show answer & solution

   Correct answer: (A) 2 and −2

   x² = 4 → x = ±2.

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