Question

Identify which of the following equations is a quadratic equation.
(A) $5x + 8 = 0$
(B) $ - 2{x^2} + x = 21$
(C) $ax + by + c = 0$
(D) None of these

Answer 1

Hint: The general form of a quadratic equation is \[a{x^2} + bx + c = 0\] where $a$ must not be equal to zero $\left( {a \ne 0} \right)$. To identify the given equations are whether quadratic or not we have to compare the given equations with the general form of a quadratic equation. If $a$ in the given equations are not equal to zero than the given equations are quadratic equations.

Complete step-by-step solution:
Here, we have to identify the quadratic equation.
(A) $5x + 8 = 0$
Comparing this equation with the general equation of a quadratic equation. We get,
$a = 0$ , $b = 5$ and $c = 8$.
Now, we get that $a = 0$ so, the given equation is not a quadratic equation.
(B) $ - 2{x^2} + x = 21$
This equation can also be written as $ - 2{x^2} + x - 21 = 0$
Comparing this equation with the general equation of a quadratic equation. We get,
$a = - 2$ , $b = 1$ and $c = - 21$.
Now, we get that $a \ne 0$ so, the given equation is a quadratic equation in variable $x$.
(C) $ax + by + c = 0$
Here, there are two variables $x$ and $y$. The degree of either of variable $x$ or $y$ is $1$.
So, the given equation is a linear equation in two variables.
Thus, the equation given in option (B) is a quadratic equation.

Hence, option (B) is correct.

Note: Similarly, if we have to identify the given equations are whether cubic/ biquadratic or not. We have to simply compare with the general equation of the cubic/ biquadratic equation.
The general form of the cubic equation is $a{x^3} + b{x^2} + cx + d = 0$. Where $a \ne 0$.
The general form of biquadratic equation is $a{x^4} + b{x^3} + c{x^2} + dx + e = 0$. Where $a \ne 0$.
Any polynomial is called a quadratic polynomial if the degree of the polynomial is $2$.