| Assertion (A): A monic quadratic polynomial having 5 and \[-3\] as zeroes is \[{{\text{x}}^{\text{2}}}-\text{2x}-\text{15}\]. |
| Reason (R): The monic quadratic polynomial having a and (3 as zeroes is given by \[p(x)={{x}^{2}}-(\alpha +\beta )x+\alpha \beta \]. |
A) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
B) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
C) Assertion (A) is true but reason (R) is false.
D) Assertion (A) is false but reason (R) is true.
Correct Answer: A
Solution :
| [a] Reason is clearly true. |
| Let \[\alpha =5\] and \[\beta =-3\] |
| Then, \[\alpha +\beta =2\] and \[\alpha \beta =-15\] |
| \[\therefore \] Required polynomial is given by |
| \[p(x)={{x}^{2}}-2x-15\] |
| \[\therefore \] Assertion: True; Reason: True and it is the correct explanation of assertion. |
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