MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Quadratic Equations

State whether...

Question

State whether $3 x + \frac{1}{x} - 8 = 0$ is a quadratic equation.

Open in App

Solution

Step 1: Definition of a quadratic equation
The standard form of a quadratic equation is $a x^{2} + b x + c = 0$ .
For a given equation to be a quadratic equation, $a \neq 0$ . and the highest power of the variable in the equation should be $2$ .
Step 2: To check whether the equation is a quadratic equation
Writing the given equation $3 x + \frac{1}{x} - 8 = 0$ in standard form of quadratic equation.
$\begin{array}{rcl} 3 x + \frac{1}{x} - 8 & = & 0 \\ \Rightarrow & 3 x^{2} + 1 - 8 x = 0 \\ \Rightarrow & 3 x^{2} - 8 x + 1 = 0 \end{array}$
On comparing this equation with the standard form $a x^{2} + b x + c = 0$ , we can see that $a = 3$ and the highest power of the variable $x$ is $2$ .
Hence, the equation $3 x + \frac{1}{x} - 8 = 0$ is a quadratic equation.

Suggest Corrections

thumbs-up

2

Similar questions

State whether $18 x^{2} - 6 x = 0$ is a quadratic equation.

Q. Check whether

3 x - 10 = 0

is a quadratic equation or not?

The following equation is a quadratic equation.

x^{2} - 3 x = 0

(state true of false)

State whether $\frac{3 x}{4} - \frac{5 x^{2}}{8} = \frac{7}{8}$ is a quadratic equation.

Q. (1)
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(i)

x^{2} - 3 x + 4 = 0

(2)
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(ii)

2 x^{2} + x - 1 = 0

(3)
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(iii)

2 x^{2} - 6 x + \frac{9}{2} = 0

(4)
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(iv)

3 x^{2} - 4 x + 1 = 0

(5)
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(v)

(x + 4)^{2} - 8 x = 0

(6)
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(vi)

(x - \sqrt{2})^{2} - 2 (x + 1) = 0

(7)
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(vii)

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

(8)
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(viii)

x (1 - x) - 2 = 0

(9)
State whether the following quadratic equation have two distinct real roots. Justify your answer
(ix)

(x - 1) (x + 2) + 2 = 0

(10)
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(x)

(x + 1) (x - 2) + x = 0

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Introduction

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Quadratic Equations

Standard X Mathematics

Join BYJU'S Learning Program

CrossIcon