Quadratic Expressions and Equations

60.
The diagram shows triangle X Y Z .
X Y = ( x + 5 ) cm and Y Z = 4 x cm.
The area of the triangle is 100 cm2.
Triangle XYZ with XY = (x+5) cm and YZ = 4x cm

(a) Use the information on the diagram to form an equation in x and show that it simplifies to:
x 2 + 5 x − 50 = 0
(a) ......................... [2]
(b) Solve:
x 2 + 5 x − 50 = 0
(b) x = ......................... or x = ......................... [3]
(c) Write down the length of the base and height of the triangle.
(c) base = ......................... cm height = ......................... cm [2]
Paper 2
61.
Factorise completely:
(a) x y 2 − x
(a) ......................... [2]
(b) 3 x 2 + 4 x − 4
(b) ......................... [2]
Paper 2
62.
Factorise completely:
(a) x 2 + 6 x − 16
(a) ......................... [2]
(b) 2 x 2 + x y − x − 2 y − 6
(b) ......................... [3]
Paper 2
63.
Factorise completely:
(a) 20 a x − b y − 5 a y + 4 b x
(a) ......................... [2]
(b) 2 x 2 − 18 and hence find the prime factors of 182.
(b) ......................... [3]
Paper 2
64.
Find the quadratic equation whose solutions are x = − 3 and x = 5 .
......................... [2]
Paper 2
65.
(a) Solve:
3 x − 2 + 3 x = 10
(a) ......................... [3]
(b) Factorise:
6 x 2 + 5 x − 6
(b) ......................... [2]
Paper 2
66.
(a) 2 u 2 + 5 u − 3
(a) ......................... [2]
(b) Factorise fully:
3 x 2 − 13 x − 10
(b) ......................... [2]
Paper 2