Question

Identify whether the given equation is quadratic or not
$4{{k}^{2}}-2k=0$

Answer 1

Hint: Quadratic equations are the polynomial equations of degree $2$ in one variable of type $f(x)=a{{x}^{2}}+bx+c$ where $a,b,c\in R$ and $a\ne 0$.
It is the general form of a quadratic equation where ‘$a$’ is called the leading coefficient and ‘$c$’ is called the absolute term of $f(x)$. The values of $x$ satisfying the quadratic equation are the roots of the quadratic equation $(\alpha ,\beta )$.

Complete step-by-step answer:
Quadratic equations are the polynomial equations of degree $2$ in one variable of type $f(x)=a{{x}^{2}}+bx+c$ where $a,b,c\in R$ and $a\ne 0$.
It is the general form of a quadratic equation where ‘$a$’ is called the leading coefficient and ‘$c$’ is called the absolute term of $f(x)$. The values of $x$ satisfying the quadratic equation are the roots of the quadratic equation $(\alpha ,\beta )$.
The quadratic equation will always have two roots. The nature of roots may be either real or imaginary.
A quadratic polynomial, when equated to zero, becomes a quadratic equation. The values of $x$ satisfying the equation are called the roots of the quadratic equation.
Now we are given an equation, $4{{k}^{2}}-2k=0$.
Comparing $4{{k}^{2}}-2k$ with $a{{x}^{2}}+bx+c$ we get,
$a=4,$ $b=-2$ and $c=0$
Also, we can see that the equation $4{{k}^{2}}-2k=0$ has degree $2$.
Therefore, we can say that $4{{k}^{2}}-2k=0$ is a quadratic equation.

Additional information:
Quadratics or quadratic equations can be defined as a polynomial equation of a second degree, which implies that it comprises a minimum one term that is squared. The definite form is$f(x)=a{{x}^{2}}+bx+c$ ; where $x$ is an unknown variable and $a,b,c\in R$are numerical coefficients Here, $a\ne 0$ because if it equals to zero then the equation will not remain quadratic anymore and it will become a linear equation, such as $bx+c=0$. The solutions to the quadratic equation are the values of unknown variables $x$, which satisfy the equation. These solutions are called roots or zeros of quadratic equations.

Note: Quadratics or quadratic equations can be defined as a polynomial equation of a second degree, which implies that it comprises a minimum one term that is squared. You can identify different equations on this basis.