Worksheet 1 Quadratic equations

Find the discriminant of each of the following quadratic equations. Solve using quadratic formula.

1.   x2 + 3x – 4 = 0

2.  7x2 + 21x − 28 = 0

3. −x2 + 4x − 7 = 0

4. x2 + -14x + 45 = 0

5.  

Solve each equation by completing the square.

1.  p2 + 14 p − 38 = 0

2.  v2 + 6v − 59 = 0

3.  a2 + 14a − 51 = 0

4.  3x2 − 12x + 11 = 0

5.  2x2 + 6x + 5 = 0

Solve the following

1. One side of a right triangle is 12 cm while the hypotenuse is  cm. Find the length of the other side.

2.Suppose that one side of a right triangle is 1 more than the other side and the hypotenuse is 1 less than 2 times the shorter side. Find the lengths of all the sides.

3. Find two positive consecutive odd integers whose product is 195.

4. The width of a rectangle is 16 cm less than 3 times the length. If the area is 35 square cm, find the dimensions of the rectangle.

5. A ladder is resting against a wall. The top of the ladder touches the wall at a height of 15 feet. Find the distance from the wall to the bottom of the ladder if the length of the ladder is one metre more than twice its distance from the wall.