**Class X Math**

Sample Paper for Quadratic Equations

**1.** By increasing the list price of a book by Rs. 10, a person can buy 10 books less for Rs. 1200. Find the original list price of the book.

**2.** A passenger train takes 2 hours less for a journey of 300 km, if its speed is increased by 5 km/hr from its usual speed. Find its usual speed.

**3.** The numerator of a fraction is one less than its denominator. If three is added to each of the numerator and denominator, the fraction is increased by

Find the fraction.

**4.** The difference of squares of two natural numbers is 45. The square of the smaller number is four times the larger number. Find the numbers.

**6.** Using quadratic formula, solve the following for x:

9x^{2} – 3(a^{2} + b^{2})x + a^{2}b^{2} = 0

**7.** The sum of the squares of two consective odd numbers is 394. Find the numbers.

**9.** Find the roots of the following quadratic equation:

**10.** Find the roots of the equation:

**11.** A natural number when subtracted from 28, becomes equal to 160 times its reciprocal. Find the number.

**12.** Find two consecutive odd positive integers, sum of whose squares is 290.

**13.** Find the values of k for which the quadratic equation

(k + 4)x^{2} + (k + 1)x + 1 = 0 has equal roots. Also find these roots.