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Question

# What are the condition(s) for (a2âˆ’4)xdâˆ’2+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 realThe 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, (a2−4), b and c should be real which follows that a,b and c are real. [If (a2−4) 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, (a2−4) should not be zero. a2−r≠0 a2≠4 a≠2,−2 So, the correct options are A,C and D.

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