Quadratic Equations Test

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Quadratic Equations Test - 16

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following is a quadratic equation ?

A
$x^{\frac{1}{2}}+2x+3=0$

B
$(x^2-1)(x+4)=x^{2}+1$

C
$x^{2}-3x+5=0$

D
$(2x^2+1)(3x-4)=6x^{2}+3$

Solution

Standard form of a quadratic equation is $ax^{2}+bx+c=0$

The quadratic equation is an equation having $2$ highest degree of the variable, which is possible only in the equation $x^2-3x+5=0$ out of the four given equations.

Hence, $Op-C$ is correct.
Question 2
1 / -0

The condition for $px^{2}+qx+r=0$ to be pure quadratic is:

A
$p=0$

B
$q=0$

C
$r=0$

D
$p=q=0$

Solution

A quadratic equation in which the term containing x raised to the power of 1 is not present is called a pure quadratic equation. In other words, ax^2 + c = 0 is a pure quadratic equation.
$\therefore\ q\ = 0$
Question 3
1 / -0

The mentioned equation is in which form?
$\cfrac {3}{4}y^{2}\, =\, 2y\, +\,7$

A
cubic

B
quadratic

C
linear

D
none of these

Solution

Given equation is $\dfrac {3}{4}y^2=2y+7$
The highest power of $x$ is $2$ . Thus, it is a quadratic equation.
Question 4
1 / -0

The mentioned equation is in which form?
$(y\, -\, 2)\, (y\, +\, 2)\, =\, 0$

A
cubic

B
quadratic

C
linear

D
none of these

Solution

Given, $(y -2)(y +2) =0$
$\Rightarrow y^2 - 4 = 0$
The highest power of $y$ is $2$ .
Thus, it is a quadratic equation.
Question 5
1 / -0

The mentioned equation is in which form?
$m^{3}\, +\, m\, +\, 2\, =\, 4m$

A
Linear

B
Quadratic

C
Quartic

D
None

Solution

No. The highest power of m is 3. Thus, it is not a quadratic equation.
Question 6
1 / -0

The mentioned equation is in which form?
$y^{2}\, -\, 4\, =\, 11y$

A
Quadratic

B
linear

C
Cubic

D
None

Solution

Given equation is $y^2-4=11y$
The highest power of $y$ is $2$ . Thus, it is a quadratic equation.
Question 7
1 / -0

The mentioned equation is in which form?
$z\, -\, \cfrac{7}{z}\, =\, 4z\, +\, 5$

A
Linear

B
Quadratic

C
cubic

D
None of these

Solution

Given,
$z - \dfrac{7}{z} = 4z + 5$

$\Rightarrow \dfrac { { z }^{ 2 }-7 }{ z } =4z+5$

$\Rightarrow z^2 - 7 = 4z^2 + 5z$

$\Rightarrow 3z^2 + 5z + 7 = 0$

The highest power of z is 2. Hence, it is a quadratic equation.
Question 8
1 / -0

The mentioned equation is in which form?
$n\, -\, 3\, =\, 4n$

A
linear

B
Quadratic

C
constant

D
None

Solution

No. The highest power of y is 1. Thus, it is not a quadratic equation.
Question 9
1 / -0

STATEMENT - 1 : $(x-2)(x+1)$ $=$ $(x-1)(x+3)$ is a quadratic equation.
STATEMENT - 2 : If $p(x)$ is a quadratic polynomial, then $p(x)$ $=$ $0$ is called a quadratic equation.

A
Statement - 1 is True, Statement - 2 is True, Statement - 2 is a correct explanation for Statement - 1

B
Statement - 1 is True, Statement - 2 is True : Statement 2 is NOT a correct explanation for Statement - 1

C
Statement - 1 is True, Statement - 2 is False

D
Statement - 1 is False, Statement - 2 is True

Solution

Given equation $(x-2)(x+1)=(x-1)(x+3)$
To find whether the given equation is a quadratic equation or not
Sol:
$(x-2)(x+1)=(x-1)(x+3)\\\implies x^2+x-2x-2=x^2+3x-x-3\\\implies x^2-x^2+x-2x-3x+x-2+3=0\\\implies -3x+1=0$
This is not a quadratic equation as an equation of degree two is called a quadratic equation.
And, a polynomial when equated to zero or some value becomes an equation.
Question 10
1 / -0

Is the following equation quadratic?
$n^{3}\, -\, n\, +\, 4\, =\, n^{3}$

A
Yes

B
No

C
Ambiguous

D
Data insufficient

Solution

A quadratic equation is a second-order polynomial equation in a single variable $x$ .
$ax^2+bx +c=0$ where $a\neq 0$ .

The equation $n^3 - n + 4 = n^3$ can be framed as $-n + 4 =0$ by subtracting ${ n }^{ 3 }$ on both sides,
Thus, it is not a quadratic equation as it is not an equation of degree $2.$

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Quadratic Equations Test - 16

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Quadratic Equations Test - 16

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Question 1

x12+2x+3=0x^{\frac{1}{2}}+2x+3=0x21​+2x+3=0

(x2−1)(x+4)=x2+1(x^2-1)(x+4)=x^{2}+1(x2−1)(x+4)=x2+1

x2−3x+5=0x^{2}-3x+5=0x2−3x+5=0

(2x2+1)(3x−4)=6x2+3(2x^2+1)(3x-4)=6x^{2}+3(2x2+1)(3x−4)=6x2+3

Solution

Question 2

p=0p=0p=0

q=0q=0q=0

r=0r=0r=0

p=q=0p=q=0p=q=0

Solution

Question 3

cubic

quadratic

linear

none of these

Solution

Question 4

cubic

quadratic

linear

none of these

Solution

Question 5

Linear

Quadratic

Quartic

None

Solution

Question 6

Quadratic

linear

Cubic

None

Solution

Question 7

Linear

Quadratic

cubic

None of these

Solution

Question 8

linear

Quadratic

constant

None

Solution

Question 9

Statement - 1 is True, Statement - 2 is True, Statement - 2 is a correct explanation for Statement - 1

Statement - 1 is True, Statement - 2 is True : Statement 2 is NOT a correct explanation for Statement - 1

Statement - 1 is True, Statement - 2 is False

Statement - 1 is False, Statement - 2 is True

Solution

Question 10

Yes

No

Ambiguous

Data insufficient

Solution

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$x^{\frac{1}{2}}+2x+3=0$

$(x^2-1)(x+4)=x^{2}+1$

$x^{2}-3x+5=0$

$(2x^2+1)(3x-4)=6x^{2}+3$

$p=0$

$q=0$

$r=0$

$p=q=0$