| Assertion (A): If the sum and product of zeroes of a quadratic polynomial is 3 and \[-2\] respectively, then the quadratic polynomial is\[{{x}^{2}}-3x-2\] |
| Reason (R): If S is the sum of zeroes and P is the product of zeroes of a quadratic polynomial then the quadratic polynomial is given by \[{{x}^{2}}-Sx+P\]. |
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] Let the quadratic polynomial be \[a{{x}^{2}}+bx+c\] and its zeroes be \[\alpha \] and \[\beta \]. |
| Now, given \[\alpha +\beta =3=S\]and \[\alpha \beta =-2=P\] |
| \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,S=3\]and \[P=-2\] |
| So, one of the quadratic polynomial is\[{{x}^{2}}-3x-2\]. |
| \[\therefore \] Assertion: True; Reason: True and it is the correct explanation of assertion. |
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