Solving Quadratic Equations

Solving Quadratic Equation by Completing the Square

x² – 6x + 5 = 0

Move constant term to the right side. x² – 6x = – 5

Divide the coefficient of x by 2. (– 6) / 2 = – 3.

Square it. (– 3)² .

Add it on both sides.

x² – 6x + (–3)² = – 5 + (–3)²

(x – 3)² = 4

x – 3 = 2 or x – 3 = – 2

x = 2 + 3 or x = – 2 + 3

x = 5 or x = 1

Solving Quadratic Equation by Formula

Finding Roots - Interactive

Questions

Q1) One root of the equation x² + kx + 8 = 0 is x = – 2. Find the value of k and the value of another root.

Q2) Solve by completing the square : x² – 10x + 24 = 0

Q3) Solve by completing the square : 2x² – x – 3 = 0

Q4) Solve Q2 & Q3 by Quadratic Formula and compare your answers.

Q5) Two consecutive, positive integers when multiplied together gives 132.

(i) Taking the smaller integer as x, form an equation and show that it reduces to x² + x – 132 = 0.

(ii) Solve this equation and find the integers.

Q6) Town P and Q are 50 km apart. John cycled from P to Q at an average speed of x km/h.

(i) Write down an expression, in terms of x for the number of hours John took to travel from P to Q.

(ii) In his return trip, his average speed in reduced by 2 km/h. Write down an expression, in terms of x for the number of hours John took to travel from Q to P.

(iii) His return trip took 50 minutes longer, form an equation in x and show that it reduced to x² – 2x – 120 = 0.

(iv) Solve this equation and find his average from Town P to Town Q.