Grade B Deduce Quadratic Roots Deduce quadratic roots

Grade B Deduce Quadratic Roots Deduce quadratic roots algebraically. If you have any questions regarding these resources or come across any errors, please contact helpful-report@pixl. org. uk

Key Vocabulary Equation Factorising Simplify Solve Quadratic Formula

How to factorise a quadratic. 1) x 2 + 7 x + 10 Find two numbers whose product is +10 and sum is +7 x 2 + 7 x + 10 5× 2=10 5+2=7 (x + 5)(x + 2) 2) x 2 + 9 x + 18 Find two numbers whose product is +18 and sum is +9 x 2 + 9 x + 18 6× 3=18 6+3=9 (x + 6)(x + 3)

How to solve a factorised equation. 3) x 2 + 7 x + 10 = 0 Factorised: (x + 5)(x + 2) = 0 x + 5 = 0 Question: - 5 How can you 4) x 2 + 9 x + 18 = 0 (x + 6)(x + 3) = 0 x + 6 = 0 - 6 x = -5 x + 2 = 0 x = -2 x = -6 x + 3 = 0 x = -3 eliminate +5?

How to solve a quadratic equation using the quadratic formula. • a b c

How to solve a quadratic equation using the quadratic formula continued … • This process is called simplifying.

How to simplify and solve quadratic equations – Now you try … 1) Factorise and solve these: a) x 2 + 2 x - 15 = 0 b) x 2 - 7 x + 6= 0 c) x 2 + 5 x + 6 = 0 d) x 2 - 4 = 0 2) Solve the quadratic equation to 2 decimal places x 2 - 7 x + 3= 0 3) Solve the quadratic equation to 2 decimal places 2 x 2 + x - 7= 0 4) Solve the quadratic equation to 2 decimal places -6 x 2 -3 x + 6= 0

How to simplify and solve quadratic equations – Now you try … 1) Factorise and solve these: a) x 2 + 2 x - 15 = 0 x= -5, x= 3 x= 6, x= 1 b) x 2 - 7 x + 6= 0 x= -3, x= -2 c) x 2 + 5 x + 6 = 0 x= 2, x= -2 d) x 2 - 4 = 0 2) Solve the quadratic equation to 2 decimal places x 2 - 7 x + 3= 0 x= 6. 54, x= 0. 46 3) Solve the quadratic equation to 2 decimal places 2 x 2 + x - 7= 0 x= 1. 64, x= -2. 14 4) Solve the quadratic equation to 2 decimal places -6 x 2 -3 x + 6= 0 x=0. 78, x= -1. 28

Problem Solving and Reasoning The area of a rectangle is 80 cm 2 The width of the rectangle is x + 1 The length of the rectangle is 2 x + 4 Solve for x and hence find the length and width of the rectangle in cm.

Problem Solving and Reasoning The area of a rectangle is 80 cm 2 The width of the rectangle is x + 1 The length of the rectangle is 2 x + 4 Solve for x and hence find the length and width of the rectangle in cm. Area of square = width × length = 80 cm 2 (2 x + 4)(x + 1) = 80 2 x 2 + 6 x + 4 = 80 2 x 2 +6 x – 76 = 0 a=2, b=6, c=-76 A length can’t be negative therefore we ignore this solution

Reason and explain § What would a negative value discriminant suggest about a quadratic? § What is the smallest and largest number of roots a quadratic can have? True or false? The roots to the equation x 2 + x – 6 are x = 2 and x = -3