Quadratic Equation (One Variable)

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

Click on each question to see answer & solution.

Question No: #11

The roots of the equal are `3x^2-12x+10=0` - (a) irrational and unequal, (b) rational and equal, (c) real and unequal, (d) not real

Question No: #12

The roots of the equation `6x^2+5x+2=0` are -
(a) real and equal, (b) real and unequal, (c) imaginary, (d) none of these.
Ans: (c) imaginary (কাল্পনিক)
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Question No: #13

State True or False. The roots of the equation `x^2+x+1=0` are real.

Question No: #14

Find the condition for which the roots of the equation `ax^2+bx+c=0` `(a\ne 0)` are -
(i) reciprocal and same sign, (ii) reciprocal and opposite sign, (iii) equal and opposite sign.

Question No: #15

If the roots of the quadratic equation `px^2+pqrx+qr=0` are reciprocal to each other, then (a) `pqr=1`, (b) `q=pr`, (c) `qr=1`, (d) `p=qr`

Question No: #16

If the roots of the equation `2x^2 + kx + (k-3) = 0` are reciprocal to each other, then the value of `k` is -
(a) 2, (b) 1, (c) 5, (d) 3
Ans: (c) 5
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Question No: #17

If the ratio of two roots of the equation `2x^2-5x+p=0` is `2:3`, then value of `p` is - (a) `2`, (b) `3`, (c) `4`, (d) `1/4`

Question No: #18

If the ratio of two roots of the equation `px^2+qx+r=0 (p\ne0)` is `m:n`, then the value of `\frac{mn}{(m+n)^2}` is - (a) `q^2/{pr}`, (b) `{pr}/q^2`, (c) `pqr`, (d) `{pq}/r^2`

Question No: #19

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`.

Question No: #20

If the ratio of roots of the equation `ax^2 + bx +c = 0` is `2:3`, then show that, `6b^2 = 25ac`.