A) c and a have opposite signs
B) c and b have opposite signs
C) c and a have the same sign
D) c and b have the same sign
Correct Answer: C
Solution :
| [c] The zeroes of the given quadratic polynomial \[a{{x}^{2}}+bx+c\] where \[c\ne 0,\]are equal, if coefficient of \[{{x}^{2}}\]and constant term have the same sign i.e., c and a have the same sign. While b i.e.. coefficient of x can be positive or negative but not zero. |
| Consider, (i) \[{{x}^{2}}+4x+4=0\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,{{(x+2)}^{2}}=0\Rightarrow x=-2,-2\] |
| and (ii) \[{{x}^{2}}-4x+4=0\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,{{(x-2)}^{2}}=0\Rightarrow x=2,2\] |
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