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 equation `x^2-2x+2=0` are `\alpha` and `\beta`, find the equation whose roots are `(\alpha+2)` and `(\beta+2)`.

Question No: #42

If `a+b+c=0`, then show that one of the roots of the equation `ax^2+bx+c=0` is `1`.

Question No: #43

A rectangular field has an area of ​​2000 square meters and perimeter of 180 meters. Find the length and width of the rectangular area.

Question No: #44

The units digit of a two-digit number is 6 more than the tens digit and product of the two digits is 12 less than the number. What could be the units digit of the number?

Question No: #45

If the product of two consecutive positive odd numbers is 143, form the equation and find the two numbers using Sridhar Acharya's formula.

Question No: #46

If the price of pens is reduced by Rs 6 per dozen, 3 more pens are available at Rs 30. Determine the cost per dozen pens before price reduction.

Question No: #47

If the speed of a boat in still water is 8 km/h, the boat travels 15 km downstream and 22 km upstream in 5 hours, find the speed of the current.

Question No: #48

Solve: `(\frac{x+4}{x-4})^2 - 5(\frac{x+4}{x-4}) + 6 = 0` [`x \ne 4`]

Question No: #49

Solve: `\frac{x}{x+1} + \frac{x+1}{x} = 2\frac{1}{12}` [`x \ne 0, -1`]

Question No: #50

Solve: `\frac{1}{x} - \frac{1}{x+b} = \frac{1}{a} - \frac{1}{a+b}` [`x \ne 0,-b`]