Quadratic Equations Level-3 Quiz-1

1. In the quadratic equation ax^2 + bx + c = 0 if the sum of the roots is equal to twice the product of the roots, then which of the following is true?

2.

3. If I had walked 1 km/hr. faster, I would have taken 10 minutes less to walk a distance of 2 km, what is the rate of my walking?

4. In a joint family there are 3 couples. The ages (all in years) of the husbands are 4x, 3x and 2x. The age of each women is 4 years less than her husband’s age. The product of the ages of the first couple is more than the sum of the products of the ages of the other two couples by 832. Find x.

5. If a number is increased by 4, then result is equal to 5 more than the twice the reciprocal of the number. Find the original number.

6. There are m ways of going from A to B, m + 3 ways of going from B to C and m + 8 ways of going from C to D. If the number of ways of going from A to D (via B and C) is 336. Find the number of ways of going from A to C.

7. (|x| – 3) (|y| + 4) = 12. How many pairs of integers (x, y) satisfy this equation?

8. Raman and Manoj attempted to solve a quadratic equation. Raman made a mistake in writing down the constant term. He ended up with the roots (4, 3). Manoj made a mistake in writing down the coefficient of x. He got the roots as (3, 2). What will be the exact roots of the original quadratic equation?

9. Find the roots of the equation x³ – 6x² + 11x – 6 = 0

10. Two of the roots of the equation x^3 – 7x^2 + 36 = 0 are such that one is thrice the other. These roots have opposite signs. Find the difference of the greatest two roots.