Chapter 4 · Quadratic Equations

NCERT Exemplar Class 10 Maths Exercise 4.1

All 11 questions of NCERT Exemplar Class 10 Maths Exercise 4.1 (Quadratic Equations), in the book's order, each with its answer and a step-by-step solution.

1. Q1
   Which of ​the ​following ​is a ​quadratic ​equation?

   1. (a)$x^2+2x+1=(4-x{)}^2+3$
   2. (b)$-2x^2=(5-x)\left(2x-\frac{2}{5}\right)$
   3. (c)$(k+1)x^2+\frac{3}{2}x=7$, where $k=-1$
   4. (d)$x^3-x^2=(x-1{)}^3$
   Show answer

   (d) $x^3-x^2=(x-1{)}^3$

   Step-by-step solution →
2. Q2
   Which ​of ​the following is not ​a quadratic equation?

   1. (a)$2(x-1{)}^2=4x^2-2x+1$
   2. (b)$2x-x^2=x^2+5$
   3. (c)$(\sqrt{2}x+\sqrt{3}{)}^2+x^2=3x^2-5x$
   4. (d)$(x^2+2x{)}^2=x^4+3+4x^3$
   Show answer

   (c) $(\sqrt{2}x+\sqrt{3}{)}^2+x^2=3x^2-5x$

   Step-by-step solution →
3. Q3
   Which of ​the following ​equations has $2$ ​as ​a ​root?

   1. (a)$x^2-4x+5=0$
   2. (b)$x^2+3x-12=0$
   3. (c)$2x^2-7x+6=0$
   4. (d)$3x^2-6x-2=0$
   Show answer

   (c) $2x^2-7x+6=0$

   Step-by-step solution →
4. Q4
   If $\frac{1}{2}$ is ​a root of the ​equation $x^2+kx-\frac{5}{4}=0$, ​then the ​value of $k$ ​is

   1. (a)2
   2. (b)$-2$
   3. (c)$\frac{1}{4}$
   4. (d)$\frac{1}{2}$
   Show answer

   (a) 2

   Step-by-step solution →
5. Q5
   Which of the ​following ​equations has ​the ​sum ​of its roots ​as 3?

   1. (a)$2x^2-3x+6=0$
   2. (b)$-x^2+3x-3=0$
   3. (c)$\sqrt{2}{x}^2-\frac{3}{\sqrt{2}}x+1=0$
   4. (d)$3x^2-3x+3=0$
   Show answer

   (b) $-x^2+3x-3=0$

   Step-by-step solution →
6. Q6
   Values ​of $k$ ​for ​which the quadratic ​equation $2x^2-kx+k=0$ has ​equal ​roots is

   1. (a)$0$ only
   2. (b)$4$
   3. (c)$8$ only
   4. (d)$0,8$
   Show answer

   (d) $0,8$

   Step-by-step solution →
7. Q7
   Which constant ​must ​be added ​and subtracted ​to ​solve the quadratic ​equation $9x^2+\frac{3}{4}x-\sqrt{2}=0$ by ​the ​method of completing the square?

   1. (a)$\frac{1}{8}$
   2. (b)$\frac{1}{64}$
   3. (c)$\frac{1}{4}$
   4. (d)$\frac{9}{64}$
   Show answer

   (b) $\frac{1}{64}$

   Step-by-step solution →
8. Q8
   The ​quadratic ​equation $2x^2-\sqrt{5}x+1=0$ ​has

   1. (a)two distinct real roots
   2. (b)two equal real roots
   3. (c)no real roots
   4. (d)more than 2 real roots
   Show answer

   (c) no real roots

   Step-by-step solution →
9. Q9
   Which ​of ​the ​following equations has ​two distinct ​real ​roots?

   1. (a)$2x^2-3\sqrt{2}x+\frac{9}{4}=0$
   2. (b)$x^2+x-5=0$
   3. (c)$x^2+3x+2\sqrt{2}=0$
   4. (d)$5x^2-3x+1=0$
   Show answer

   (b) $x^2+x-5=0$

   Step-by-step solution →
10. Q10
    Which ​of the following equations ​has no ​real ​roots?

    1. (a)$x^2-4x+3\sqrt{2}=0$
    2. (b)$x^2+4x-3\sqrt{2}=0$
    3. (c)$x^2-4x-3\sqrt{2}=0$
    4. (d)$3x^2+4\sqrt{3}x+4=0$
    Show answer

    (a) $x^2-4x+3\sqrt{2}=0$

    Step-by-step solution →
11. Q11
    $(x^2+1{)}^2-x^2=0$ has

    1. (a)four real roots
    2. (b)two real roots
    3. (c)no real roots
    4. (d)one real root
    Show answer

    (c) no real roots

    Step-by-step solution →