  Question

What is/are the condition(s) for (a2−4)xd−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  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, (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. Mathematics

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