Question

Which one of the following is not a quadratic equation?
$
  \left( {\text{i}} \right){x^2} = 6x \\
  \left( {{\text{ii}}} \right){x^2} - 6x = 30 \\
  \left( {{\text{iii}}} \right){x^2} = 10 \\
  \left( {{\text{iv}}} \right)x = 1 \\
$

Answer 1

Hint: You have to check which is not a quadratic equation. The general form of the quadratic equation is $y = a{x^2} + bx + c$ where $a \ne 0$. So you have to check whether the coefficient of ${x^2}$is $0$ or not.

So we will check every option one by one.
$\left( {\text{i}} \right){x^2} = 6x$
Here in this option, when we compare with general form of quadratic equation $y = a{x^2} + bx + c$
here only $c = 0$ so it is clearly a quadratic equation, because it does not depend on $c$.
$\left( {{\text{ii}}} \right){x^2} - 6x = 30$
When we compare this equation with general form of quadratic equation $y = a{x^2} + bx + c$
 we have all the values in this equation. So it is clearly a quadratic equation.
$\left( {{\text{iii}}} \right){x^2} = 10$
When we compare this equation with general form of quadratic equation $y = a{x^2} + bx + c$
here only $b = 0$, so it is also a quadratic equation. Because it does not depend on $b$.
$\left( {{\text{iv}}} \right)x = 1$
Here in this option, when we compare with general form of quadratic equation $y = a{x^2} + bx + c$
The coefficient of ${x^2}$ is $0$ that means $a = 0$ so it is not a quadratic equation.
Hence the option $\left( {{\text{iv}}} \right)$is the correct option.

Note:Whenever you get these types of questions the key concept of solving is you have to compare with the general form of quadratic equation. You may directly check by noticing the coefficient of ${x^2}$. If the coefficient of ${x^2}$ is not equal to $0$ that means it is a quadratic equation.