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

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1. The roots of a quadratic equation $x^{2}-4 \sqrt{3} x+9=0$ are:

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2. The roots of a quadratic equation $x^{2}-9 x+18=0$ are:

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

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

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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:

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6. If $\alpha, \beta$ are the roots of a quadratic equation $x^{2}+x-2=0$, then value of $\frac{1}{\alpha}+\frac{1}{\beta}$ is:

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

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

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

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

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

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

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

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

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15. The discriminant of a quadratic equation $3 x^{2}-2 x+\frac{1}{3}=0$ is :

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