Quadratic Equation (One Variable)

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

Click on each question to see answer & solution.

Question No: #41

If the roots of the quadratic equation `5x^2-2x+3=0` are `\alpha` and `\beta`, then find the value of `\alpha^{-1} + \beta^{-1}`.

Question No: #42

If the roots of quadratic equation `5x^2+2x-3=0` are `\alpha` and `\beta`, then find the value of `(\frac{\alpha^2}{\beta}+\frac{\beta^2}{\alpha})`.

Question No: #43

If the roots of the equation `ax^2 + bx + c = 0` (`a \ne 0`) are equal, then -
(a) `b = -2ac`, (b) `b = 2ac`, (c) `b^2 = 4ac`, (d) `b^2 = -4ac`
Ans: (c) `b^2 = 4ac`
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Question No: #44

If the roots of the equation `9x^2+6x+a=0` are real and equal, then the valie of `a` is - (a) `- 2/3` , (b) `1/9` , (c) `1`, (d) `9`

Question No: #45

for which value of `k`, roots of the quadratic equation `9x^2+3kx+4=0` are real and equal?
Ans: `\pm 4`
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Question No: #46

Find the values of `p`, for which the quadratic equation `x^2+(p-3)x+p=0` has real and equal roots.
Ans: `p = 1,9`
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Question No: #47

Find the values of `k`, for which the roots of the quadratic equation `(3k+1)x^2+2(k+1)x+k=0` are real and equal.
Ans: `k = - 1/2, 1`
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Question No: #48

For which values of `a`, the roots of the quadratic equation `x^2-(3a-1)x+2a^2+2a-11=0` are real and equal?
Ans: `a = 5, 9`
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Question No: #49

Show that, for `a=b`, the equation `2(a^2+b^2)x^2+2(a+b)x+1=0` has no real roots.

Question No: #50

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`.