Question

What is the standard form of the quadratic equation: $n - \dfrac{7}{n} = 4$
$A){n^2} + 4n - 7 = 0$
$B){n^2} - 4n - 7 = 0$
$C){n^2} - 4n + 7 = 0$
$D)$ None of these

Answer 1

First, we need to know about the concept of quadratic equations. Quadratic equations are equations that are often called the second degree. It means that it consists of at least one term which is squared. Because of these reasons, it is known as the quad meaning square. The general quadratic equation is $a{x^2} + bx + c = 0$

Complete step-by-step solution:
To solve the given equation, we must know about the operations in mathematics.
Since multiplicand refers to the number multiplied. Also, a multiplier refers to the number that multiplies the first number. Have a look at an example; while multiplying $5 \times 7$ the number $5$ is called the multiplicand and the number $7$ is called the multiplier. The process of the inverse of the multiplication method is called division. Like $x \times y = z$ is multiplication thus the division sees as $x = \dfrac{z}{y}$. We usually need to memorize the
multiplication tables in childhood so it will help to do mathematics.
Since from the given we have $n - \dfrac{7}{n} = 4$ and now multiply the values with $n$ using the multiplication operation then we have $n \times n - \dfrac{7}{n} \times n = 4 \times n$ and now cancel the common terms using the division operation then we have $n \times n - \dfrac{7}{n} \times n = 4 \times n \Rightarrow {n^2} - 7 = 4n$
Now equate all the values on the left sides or subtract the values with $- 4n$, then we have $\Rightarrow {n^2} - 7 - 4n = 0$ (by the subtraction operation)
Therefore, we get the simplification as ${n^2} - 7 - 4n = 0$
Hence the option $B){n^2} - 4n - 7 = 0$ is correct.

Note: In the quadratic equation, there is no possibility of $a = 0$ in the equation $a{x^2} + bx + c = 0$. Because if $a = 0$ then we get $bx + c = 0$ but which is degree one equation and linear and hence $a \ne 0$ is the main rule in the quadratic equation.