InterviewSolution
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InterviewSolution
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Which of the following equations has two distinct real roots?A. `2x^(2)-3sqrt(2)x+9/4=0`B. `x^(2)+x-5=0`C. `x^(2)+3x+2sqrt(2)=0`D. `5x^(2)-3x+1=0` |
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Answer» The given equation is `x^(2)+x-5=0` On comparing with `ax^(2)+bx+c=0` we get `a=1, b=1` and `c=-5` The discriminant of `x^(2)+x-5=0` is `D=b^(2)-4ax=(1)^(2)-4(1)(-5)` `=1+20=21` `implies b^(2)-4acgt0` So `x^(2)+x-5=0` has two distinct real roots. (a) Given equation is `2x^(2)-3sqrt(2)x+9//4=0` On comparing with `ax^(2)+bx+c=0` `a=2,b=-3sqrt(2)` and `c=9//4` Now `D=b^(2)-4ac=(-3sqrt(2))^(2)-4(2)(9//4)=18-18=0` Thus, the equation has real and equal roots. (c) Given equation is `x^(2)+3x+2sqrt(2)=0` On comparing with `ax^(2)+bx+c=0` `a=1,b=3` and `c=2sqrt(2)` Now `D=b^(2)-4ac=(3)^(2)-4(1)(2sqrt(2))=9-8sqrt(2)lt0` `:.` Roots of the equation are not real. (d) Given equation is `5x^(2)+3x+1=0` On comparing with `ax^(2)+bx+c=0` `a=5,b=-3, c=1` Now `D=b^(2)-4ac=(-3)^(2)-4(5)(1)=9-20lt0` Hence roots of the equation are not real. |
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