A) {2, -5}
B) {-3, 2}
C) {-2, 5}
D) {3, -5}
Correct Answer: C
Solution :
Given quadratic eqn. is \[{{x}^{2}}+px+\frac{3p}{4}=0\] So, \[\alpha +\beta =-p,\alpha \beta =\frac{3p}{4}\] Now, given \[|\alpha -\beta |\,=\sqrt{10}\] \[\Rightarrow \]\[\alpha -\beta =\pm \sqrt{10}\] \[\Rightarrow \]\[{{(\alpha -\beta )}^{2}}=10\Rightarrow {{\alpha }^{2}}+{{\beta }^{2}}-2\alpha \beta =10\] \[\Rightarrow \]\[{{(\alpha +\beta )}^{2}}-4\alpha \beta =10\] \[\Rightarrow \]\[{{p}^{2}}-4\times \frac{3p}{4}=10\Rightarrow {{p}^{2}}-3p-10=0\] \[\Rightarrow \]\[p=-2,5\Rightarrow p\in \{-2,5\}\]
You need to login to perform this action.
You will be redirected in
3 sec
