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Question

What is/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 a0 [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 d2. So, d2=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.


Mathematics

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