A) 2 and 6
B) 3 and 4
C) 2 and 8
D) 2 and 5
Correct Answer: A
Solution :
| Let the zeroes of the quadratic polynomial are \[\alpha \] and \[\beta \] |
| \[\alpha +\beta =8\] (i) |
| And \[\alpha \,.\,\beta =12\] (ii) |
| Substitute value of \[\beta =8-\alpha \]in Eq. (ii) |
| \[\alpha \left( 8-\alpha \right)=12\] |
| \[{{\alpha }^{2}}-8\alpha +12=0\] |
| \[{{\alpha }^{2}}-6\alpha -2\alpha +12=0\] |
| \[\alpha \left( \alpha -6 \right)-2\left( \alpha -6 \right)=0\] |
| \[\alpha =6,\,\alpha =2\] |
| If \[\alpha =6\], then \[\beta =2\] |
| If \[\alpha =2\], then \[\beta =6\] |
| Hence, the two zeroes are 2 and 6. |
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