Question

The necessary condition for ax2

+ bx + c = 0; where a, b, c ∈ R to be a quadratic

Equation (QE) is ______.

(A) a = 0 (B) a ≠ 0 (C) a = 1 (D) a ≠ 1​

Answer 1

(B) a not equal 0

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Answer 2

Answer:

Option (B) is the correct answer.

Step-by-step explanation:

Quadratic equation:-

• The polynomial equation of degree 2 in one variable of the type $ax^2+bx+c=0$, where $a,b,c$ ∈ R and a ≠ 0

Step 1 of 1

To find:-

The necessary condition for $ax^2+bx+c=0$, where $a,b,c$ ∈ R to be a quadratic equation.

Consider the given quadratic equation as follows:

$ax^2+bx+c=0$ ____ (1)

where $a,b,c$ ∈ R

(A) a = 0

If a = 0. Then the equation (1) becomes,

$(0)x^2+bx+c=0$

$bx+c=0$

Clearly, the equation is no longer a quadratic equation.

Thus, option (A) is incorrect.

(B) a ≠ 0

Clearly, the equation (1) remains the quadratic equation.

Hence, a ≠ 0 is a necessary condition.

Thus, option (B) is correct.

(C) a = 1

If a = 1. Then the equation (1) becomes,

$(1)x^2+bx+c=0$

$x^2+bx+c=0$

Clearly, the equation still remains a quadratic equation.

But, a = 1 is not the necessary condition.

Thus, option (C) is incorrect.

(D) a ≠ 1​

If a ≠ 1​.

Then the equation (1) is still a quadratic equation.

But, a ≠ 1​ is not the necessary condition.

Thus, option (D) is incorrect.

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