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

In the equation `x^2+px+q=0`, coefficient of `x` is misprinted as `13` instead of `14`, and it turns out that roots are `-5` and `-8`. Then roots of the original equation are - (a) `-4, -10`, (b) `4, 10`, (c) `-4, 10`, (d) `4, -10`

Question No: #12

If one root of the equation `x^2-x-k=0` is square of its other root, then value of `k` is - (a) `2\pm\sqrt{3}`, (b) `3\pm\sqrt{2}`, (c) `2\pm\sqrt{5}`, (d) `5\pm\sqrt{2}`

Question No: #13

If two roots of the equation `x(x-3)=4` are `\alpha` and `\beta`, then value of `\alpha^2+\beta^2` is - (a) 14, (b) 15, (c) 16, (d) 17

Question No: #14

If `p, q, r` rational and `p+q+r=0`, then the roots of the quadratic equation `px^2+qx+r=0` are - (a) rational, (b) irrational, (c) real, (d) none of these.

Question No: #15

If the roots of `x^2+px+12=0` are `\alpha`, `\beta` and are such that `\alpha-\beta=1`, then value of `p` is - (a) `\pm2`, (b) `\pm5`, (c) `\pm6`, (d) `\pm7`

Question No: #16

If the roots of the equation `x^2-5x+6=0` are `\alpha` and `\beta`, then value of `\alpha/\beta + \beta/\alpha` is - (a) `15/2`, (b) `2/15`, (c) `6/13`, (d) `13/6`

Question No: #17

i) If the roots of the equation are `2, -3`, then write its quadratic equation.
ii) If the roots of the equation are `4\pm\sqrt{3}`, then write its quadratic equation.

Question No: #18

By applying Sridhar Acharya's formula, if the roots of the equation `5x^2+2x-7=0` are `x=\frac{k\pm12}{10}`, then find the value of `k`.

Question No: #19

If the numerical value of the roots of the equation `3x^2+(2m-1)x+(m+3)=0` are equal but opposite sign, then what will be the value of `m` ?

Question No: #20

Find the condition for which the roots of the equation `ax^2+bx+c=0` `(a\ne 0)` are reciprocal and having opposite sign to each other.