| 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] If the zeroes of the polynomial \[f\left( x \right)=\left( {{k}^{2}}+4 \right){{x}^{2}}=4kx+\left( {{k}^{3}}-9 \right)\]are equal in magnitude but opposite in sign, then value of k is zero |
| Reason [R] A quadratic polynomial whose zeroes are \[\alpha \] and \[\beta \]is \[{{x}^{2}}+\left( \alpha +\beta \right)x+\alpha \beta \] |
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 :
| Let the roots are \[\alpha\] and \[-\alpha\] |
| Sam of zero \[=\frac{-\,Coefficient\,of\,x}{Coefficient\,of\,{{x}^{2}}}\] |
| \[\alpha +\left( -\alpha \right)=\frac{-4k}{{{k}^{2}}+4}\] |
| \[0=4k\] |
| Thus, k = 0 |
| Hence, Assertion is true but Reason is false. |
You need to login to perform this action.
You will be redirected in
3 sec
