| Assertion (A): The sum and product of the zeroes of a quadratic polynomial are \[-\frac{1}{4}\] and \[\frac{1}{4}\] respectively. |
| Then the quadratic polynomial is \[4{{x}^{2}}+x+1\]. |
| Reason (R): The quadratic polynomial whose sum a product of zeroes are given is \[{{x}^{2}}-\] (sum of zeroes) \[x+\]product of zeroes). |
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] Sum of zeroes \[=-\frac{1}{4}\] |
| and product of zeroes \[=\frac{1}{4}\] |
| Quadratic polynomial be \[{{x}^{2}}-\left( -\frac{1}{4} \right)x+\frac{1}{4}\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{x}^{2}}+\frac{1}{4}x+\frac{1}{4}\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac{1}{4}(4{{x}^{2}}+x+1)\] |
| Quadratic polynomial be \[4{{x}^{2}}+x+1\] So, both assertion and reason are correct and reason explains assertion. |
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