Question

What are the condition(s) for $(a^2-4)x^{d-2}+bx+c=0$ to be a quadratic equation in x?

• A. ${}^{\prime }{a}^{\prime }$ can be ANY real number other than 2, -2
• B. $a,b,c$ are real numbers where ${}^{\prime }{a}^{\prime }$ cannot be 4 or -4
• C. $d=4$
• D. $a,b,c$ are real

Answer 1

Answer: (A), (C), (D)

$a,b,c$ are real

The standard form of any quadratic equation is $a{x}^2+bx+c=0$, provided a,b,c [coefficients] are real numbers and a≠0 [a is called the leading coefficient]. So, in the above question, let us look at the conditions one by one.

1) Coefficients should be real - which means, $(a^2-4)$, b and c should be real which follows that a,b and c are real. [If $(a^2-4)$ is real, this follows that $a^2$ is real and hence, a is real]

2) Degree of the polynomial should be 2 - in this case, the degree is given by (d-2). So, d - 2 = 4, which means d = 4.

3) Leading coefficient is non-zero a real number.
So, $(a^2-4)$ should not be zero.
$a^2-r\ne 0$
$a^2\ne 4$
$a\ne 2,-2$