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Quadratic Equation (One Variable)
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Quadratic Equation (One Variable)
All Questions (Page: 4)
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All Questions (PDF)
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Study Material (PDF)
All Questions (PDF)
Self Assesment
Sort As
Serial Number
Newly Added
Language
English
Bengali
Click on each question to see answer & solution.
Question No: #31
Find the values of `p`, for which the quadratic equation `x^2+(p-3)x+p=0` has real and equal roots.
Ans:
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Question No: #32
If the roots of the quadratic equation `(1+m^2)x^2+2mcx+(c^2-p^2)=0` are real and equal, then prove that `c^2=p^2(1+m^2)`.
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Question No: #33
Show that, for `a=b`, the equation `2(a^2+b^2)x^2+2(a+b)x+1=0` has no real roots.
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Question No: #34
If the equations `x^2+px+r=0` and `x^2+rx+p=0` (`p \ne r`) have a common root, then find the value of `1+p+r`.
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Question No: #35
If one of the roots of the equation `x^2+px+12=0` is `2` and two roots of the equation `x^2+px+q=0` are equal, then find the value of `q`.
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Question No: #36
In the quadratic equation `ax^2+bx+c=0` (`a\ne0`), if one root is double to other root, then prove that `2b^2=9ac`.
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Question No: #37
If two roots of the equation `(b-c)x^2+(c-a)x+(a-b)=0` are equal, then prove that `2b=a+c`.
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Question No: #38
Find the equation whose roots are reciprocal of the roots of `2x^2+5x+3=0`.
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Question No: #39
Find the equation whose roots are square of the roots of `x^2+x+1=0`.
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Question No: #40
Find the equation whose roots are square of the roots of `2x^2+3x+1=0`
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