Quadratic Equation (One Variable)

Study Material (PDF)
Self Assesment
Study Material (PDF)
Self Assesment

Click on each question to see answer & solution.

Question No: #31

If one of the roots of the equation `x^2-(2+b)x+6=0` is `2`, then what will be its other root?

Question No: #32

If two roots of the equation `x^2+px+q=0` are `p` and `q`, then find the value of `p` and `q`.

Question No: #33

Find the quadratic equation whose sum and product of the roots are `b/a` and `c^2/b` respectively.

Question No: #34

Equation: `x^2-x=K(2x-1)`. Find the value of `K`, if -
(i) sum of the roots is `2`,
(ii) sum and products of its roots are equal.

Question No: #35

Sum of the roots of the equation `(2-\sqrt{3})x^2-x+1=0` is ........
Ans: `(2 + \sqrt{3})`
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Question No: #36

If the product of the roots of the equation `x^2 - 5x + k = 12` is `-3`, then the value of `k` is -
(a) `9`, (b) `12`, (c) `15`, (d) `-3`
Ans: (a) `9`
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Question No: #37

If the sum and product of the roots of the equation `2x^2+2kx+3=0` are equal to each other, then the value of `k` is -
(a) `- 3/2`, (b) `3/4`, (c) `- 2/3`, (d) `2/3`
Ans: (a) `- 3/2`
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Question No: #38

For which value of `k`, sum of the square of the roots of the equation `6x^2+x+k=0` is `25/36`?
Ans: `-2`
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Question No: #39

Find the ratio of sum and product of the roots of the equation `7x^2-66x+27=0`.

Question No: #40

If the roots of the equation `x^2-22x+105=0` are `\alpha` and `\beta` , then find the value of `\alpha - \beta`.