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.

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10th Maths Online Test: Quadratic Equations

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Q. 1. The zeros of $4 x^{2}+1-4 x$ are:
	$\frac{1}{2}, \frac{1}{2}$
	$\frac{-1}{2}, \frac{-1}{2}$
	$1, \frac{1}{4}$
	$\frac{-1}{4}, 1$

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Q. 2. If $\alpha, \beta$ are the zeros of the polynomial $2 x^{2}+5 x-10$, then the value of $\alpha \beta$ is:
	$\frac{-5}{2}$
	5
	-5
	$\frac{2}{5}$

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Q. 3. The zeros of $\sqrt{3} x^{2}+10 x+7 \sqrt{3}$ are:
	$-\sqrt{3}, \frac{-7}{\sqrt{3}}$
	$-\sqrt{3}, \frac{7}{\sqrt{3}}$
	$\sqrt{3}, \frac{7}{\sqrt{3}}$
	$\frac{7}{\sqrt{3}}, \sqrt{9}$

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Q. 4. Is $(3 x+10)$ is a factor of $9 x^{3}-27 x^{2}-100 x+300$ ?
	No
	Yes
	cannot be determined
	None of these

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Q. 5. If the zeros of the quadratic polynomial $a x^{2}+b x+c, c \neq 0$ are equal then,
	$c$ and $b$ have same signs
	$c$ and $b$ have opposite signs
	$c$ and $a$ have same signs
	$c$ and $a$ have opposite signs

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Q. 6. Which one is polynomial?
	$\sqrt{x}+1$
	$\frac{1}{\dot{x}^{3}+1}$
	$\frac{1}{x^{2}+1}$
	$x^{3}+1$

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Q. 7. The zeros of $3 x^{2}-4-x$ are:
	$1, \frac{-4}{3}$
	$-1, \frac{4}{3}$
	$-1, \frac{-4}{3}$
	$1, \frac{4}{3}$

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Q. 8. The zeros of $x^{2}+3 x-(b+2)(b-1)$ are:
	$-(b+2),-(b-1)$
	$(b+2),-(b-1)$
	$-(b+2),(b-1)$
	None of these

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Q. 9. The sum of zeros of quadratic equation $2 x^{2}-8 x+6$ is:
	3
	-4
	4
	-3

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Q. 10. The product of zeros of quadratic equation $x^{2}+7 x+10$ is:
	-7
	10
	-10
	7

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