Question

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

• A. a can be ANY real number other than 2, -2
• B. a, b, c are ALL real numbers where a cannot be 4 or -4
• C. d = 4
• D. a, b, c are real

Answer 1

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

The correct options are
A a can be ANY real number other than 2, -2
C d = 4
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) The degree of the polynomial should be 2 - in this case, the degree is given by (d-2).
So, d - 2 = 2, which means d = 4.

3) Leading coefficient is non-zero a real number.
So, $(a^2-4)$ should not be zero.
$a^2-r\ne 0$
$a^2\ne 4$
$a\ne 2,-2$
So, the correct options are A,C and D.