| Directions: Each of these questions contains two statements: Assertion [A] and Reason [R]. Each of these questions also has four alternative choices, any one of which is the correct answer. You have to select one of the codes [a], [b], [c] and [d] given below. |
| Assertion [A] Zeroes of |
| \[f\left( x \right)={{x}^{2}}-4x-5\]are 5, -1 |
| Reason [R] The polynomial whose zeroes are \[2+\sqrt{3},\,2-\sqrt{3}\]is \[{{x}^{2}}-4x+7\] |
A) A is true, R is true; R is a correct explanation for A.
B) A is true, R is true; R is not a correct explanation for A.
C) A is true; R is False.
D) A is false; R is true.
Correct Answer: C
Solution :
| Assertion Given, \[f\left( x \right)={{x}^{2}}-4x-5\] |
| Splitting the middle term |
| \[f\left( x \right)={{x}^{2}}-5x+x-5\] |
| \[=x\left( x-5 \right)+1\left( x-5 \right)\] |
| \[=\left( x+1 \right)\left( x-5 \right)\] |
| \[f\left( x \right)=0\] |
| \[x\text{ }=\text{ }-1\] and x = 5 (True) |
| Reason We know that, the polynomial is |
| \[{{x}^{2}}-\left( \alpha +\beta \right)x+\alpha \,.\beta\] |
| \[{{x}^{2}}-\left( 2+\sqrt{3}+2-\sqrt{3} \right)x+\left( 2+\sqrt{3} \right).\left( 2-\sqrt{3} \right)\] |
| \[{{x}^{2}}-4x+\left( 4-3 \right)\] |
| \[{{x}^{2}}-4x+1\] |
| Assertion is true and Reason is false |
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