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Question

What are the condition(s) for (a24)xd2+bx+c=0
to be a quadratic equation in x?

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

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
ax2+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, (a24),
b and c should be real which follows that a,b and c are real.
[If (a24) is real, this follows that a2 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, (a24) should not be zero.
a2r0
a24
a2,2
So, the correct options are A,C and D.

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