A) has no linear term and the constant term is negative
B) has no linear term and the constant term is positive
C) can have a linear term but the constant term is negative
D) can have a linear term but the constant term is positive
Correct Answer: A
Solution :
| [a] Let \[p(x)={{x}^{2}}+ax+b\] |
| and by given condition the zeroes are \[\alpha \] and \[-\alpha \] |
| \[\therefore \] Sum of the zeroes \[=\alpha -\alpha =0\] |
| \[\Rightarrow \,\,\,\,\,a=0\Rightarrow p(x)={{x}^{2}}+b,\]which cannot be linear and product of zeroes \[=\alpha (-\alpha )=b\Rightarrow -{{\alpha }^{2}}=b\]which is only possible when \[b<0\]. |
| Hence, it has no linear term and the constant term is negative. |
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