Question

The condition for $p{x^2} + qx + r = 0$ to be pure quadratic is:
A.p = 0
B.q = 0
C.r = 0
D.p = q = 0

Answer 1

Hint: We will use the definition of a pure quadratic equation to determine the correct option. It generally refers to an equation which has the coefficient of x = 0.

Complete step-by-step answer:
We are given an equation $p{x^2} + qx + r = 0$.
We need a certain condition when this equation will be purely quadratic.
For this, let us define the purely quadratic equations.
Definition: A pure quadratic equation is a quadratic equation which contains no linear term. We can say that a pure quadratic equation is any equation in the form: $a{x}^{2} + c$ = 0, where a, c $ \in $ R and a $ \ne $0.
In other simpler words, a pure quadratic equation is that quadratic equation which has the coefficient of x equals to 0 in its standard form $a{x}^{2} + bx + c$ = 0 i. e., when b = 0 in this quadratic equation, it will be called a pure quadratic equation where a and c are real numbers and a $ \ne $0.
Or, we can define it as the quadratic equation having only a second degree variable and it is called a pure quadratic equation.
Hence, comparing the standard pure quadratic equation $a{x}^{2} + c$ = 0 with the given equation $p{x^2} + qx + r = 0$, we get
q = 0
therefore, for the equation $p{x^2} + qx + r = 0$ to be called a pure quadratic equation, q must be 0.
Hence, option (B) is correct.

Additional information: A pure quadratic equation can also be described as a quadratic equation having only two terms from which one is the term that contains $x^2$ and the other term is a constant.

Note: In such questions, you may get confused because such questions are totally based on the definitions of particular terms and concepts used in our chapters. You can use any definition to prove this question.