A) \[{{x}^{2}}-7x+14=0\]
B) \[{{x}^{2}}-7x+10=0\]
C) \[x+5x-6=0\]
D) \[{{x}^{2}}+5x-6=0\]
Correct Answer: B
Solution :
For quadratic equation \[a{{x}^{2}}+bx+c=0,\] Sum of roots \[=-\frac{b}{a}\] Product of roots \[=\frac{c}{a}\] For equation \[{{x}^{2}}-7x+10=0.\] Sum of roots = 7 Their product =10 i.e. \[\alpha +\beta =7,\]\[\alpha \beta =10\] \[\Rightarrow \]\[{{(\alpha -\beta )}^{2}}={{(\alpha +\beta )}^{2}}-4\alpha \beta \] \[=49-40=9\] \[\Rightarrow \alpha -\beta =3\] \[\therefore \]\[\alpha +\beta +\alpha -\beta =7+3\] \[\Rightarrow \]\[2\alpha =10\Rightarrow \alpha =5\] \[\therefore \]\[\alpha +\beta =7\Rightarrow 5+\beta =7\] \[\Rightarrow \]\[\beta =7-5=2\]
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