Quadratic Equations Test

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Quadratic Equations Test - 18

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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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Re-Attempt Weekly Quiz Competition

Quadratic Equations Test - 18

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Quadratic Equations Test - 18

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SHARING IS CARING

Question 1

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

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

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

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

Solution

Question 2

$$p=0$$

$$q=0$$

$$r=0$$

$$p=q=0$$

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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