Question

What is a pure quadratic equation? Give an example.

Answer 1

Hint: In this particular question use the concept that the power of variable in a quadratic equation is 2, or there are only one squared variable in quadratic equation and a linear variable and a constant term, but in a pure quadratic equation linear variable term is missing so use these concepts to reach the solution of the question.

Complete step by step solution:
As we all know that the general quadratic equation is given as,
$a{x^2} + bx + c = 0$
Where a, b and c are belongs to real numbers.
So as we see that in a quadratic equation there are only one squared variable in the quadratic equation and a linear variable and a constant term.
Now in a pure quadratic equation there has no linear term so we can say that a pure quadratic equation is in the form of
$ \Rightarrow a{x^2} + c = 0$
So this is the representation of a pure quadratic equation.
Where, (a) and (c) can be any real positive or negative integers.
For example: ${x^2} - 9 = 0$
Now we can solve this pure quadratic equation very easily.
$ \Rightarrow {x^2} = 9$
Now take square root on both sides we have,
$ \Rightarrow x = \sqrt 9 = \pm 3$
So this is the required answer.

Note: Whenever we face such types of questions the key concept we have to remember is that we always recall the basic property of the quadratic equation which is stated above and the basic property of pure quadratic equation which is also stated above so these are the basis of finding the pure quadratic equation.