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10th Mathematics Online Test English Medium

Chapter 4 Quadratic Equations

Class 10 Mathematics Chapter 4 Quadratic Equations Multiple Choice Questins Quiz / MCQ Quiz online test base on NCERT useful for NTSE Maths Olympiad Board Exam Important Questions.

टेस्ट में कुल प्रश्न = 10

Check your score at the end of quiz.

Each correct answer = 1 mark, wrong answer = 0 marks.

2826

1. The discriminant of a quadratic equation $x^{2}-4 x+b=0$ is:

$16-4 b$

$16+4 b$

$b^{2}-16$

$16-b^{2}$

2822

2. A quadratic equation $a x^{2}-4 a x+2 a+1=0$ has equal roots, then the value of $a$ is:

$\frac{1}{2}$

2818

3. The roots of a quadratic equation $6 x^{2}-x-2=0$ are:

$\frac{3}{2}, \frac{1}{2}$

$\frac{2}{3}, \frac{-1}{2}$

$\frac{-2}{3}, \frac{1}{2}$

None of these

2813

4. A quadratic equation $x^{2}-2 k x+9=0$ has two equal roots, then the value of $k$ is:

$\pm$9

$\pm \theta$

$\pm$ 3

$\pm$ 2

2830

5. If the roots of a quadratic equation $2 x^{2}+3 x-4=0$ are $\alpha$ and $\beta$, then the value of $\alpha+\beta$ is:

$\frac{-2}{3}$

-2

$\frac{-3}{2}$

2814

6. The roots of a quadratic equation $x^{2}-5 x+6=0$ are:

$5,-6$

2,3

$6,-1$

$-2,-3$

2815

7. The roots of a quadratic equation $3 x^{2}-2 x+\frac{1}{3}$ are:

3,2

$\frac{1}{3}, \frac{1}{3}$

$\frac{1}{3}, \frac{1}{2}$

None of these

2824

8. Which type of equation $(x+2)^{3}=\left(x^{2}-1\right) 2 x$ is ?

Linear

quadratic

cubic

None of these

2819

9. A quadratic equation $a x^{2}+b x+c=0 ; a \neq 0$ has real roots:

$b^{2}-4 a c>0$

$b^{2}-4 a c<0$

(a) and $(b)$ both

None of these

2834

10. Which of the following is a quadratic equation:

$4 x+6$

$a x^{3}-b x+c=0$

$x(x+3)=x$

$x^{2}+\frac{1}{x^{2}}=2$

2832

11. A quadratic equation $x^{2}-k x+1=0$, has no real roots:

$-2

$k>2$

$k<-2$

None of these

2821

12. The discriminant of a quadratic equation $2 x^{2}-3 x-12=0$ is:

-87

105

-33

2831

13. A quadratic equation $a x^{2}+b x+c=0$, has equal roots:

$b^{2}=4 a c$

$b^{2}=-4 a c$

$b^{2}=a c$

None of these

2833

14. A quadratic equation $a x^{2}+b x+c=0$ has real and equal roots:

$\frac{-b}{2 a}$

$\frac{b}{2 a}$

$\pm \frac{b}{2 a}$

None of these

2828

15. A quadratic equation $x^{2}+4 x+k=0$ has real roots:

$k \leq 4$

$k \geq 4$

$k \leq 1$

$k \geq 1$

Real Numebrs Chapter 1 class 10 Basic Concepts

1.Quadratic Equation:
A quadratic equation in the variable $x$ is of the form $a x^{2}+b x+c=0$, where $a, b, c$ are real numbers and $a \neq 0$.

2.Roots of a Quadratic Equation:
A real number $\alpha$ is said to be a root of the quadratic equation $a x^{2}+b x+c=0$, if $a \alpha^{2}+b \alpha+c=0$. The zeroes of the quadratic polynomial $a x^{2}+b x+c$ and the roots of the quadratic equation $a x^{2}+b x+c=0$ are the same.

3. Quadratic formula:
The roots of a quadratic equation $a x^{2}+b x+c=0$ are given by $\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$, provided $b^{2}-4 a c \geq 0$.

4. Nature of Roots of a Quadratic Equation:
A quadratic equation $a x^{2}+b x+c=0$ has

(i) two distinct real roots, if $b^{2}-4 a c>0$,

(ii) two equal roots (i.e., coincident roots), if $b^{2}-4 a c=0$, and

(iii) no real roots, if $b^{2}-4 a c<0$.