Question

A tire company has noticed how much distance it cuts before it has to change its tires. The table below
The result shows about 1000 tires.
Distance (in km) 4000 4000 to 9000 9001 to 14000
Less than 9000 14000
Version
20
210 325 445
If you don't drink, then
More than​

Answer 1

Let f(x) = ax3 + 3x2 – 3

and g(x) = 2x3 – 5x + a

∴ f(4) = a × 43 + 3 × 42 – 3

= 64a + 48 – 3

= 64a + 45

g(4) = 2 × 43 – 5 × 4 + a

= 128 – 20 + a

= 108 + a

It is given that:

f(4) = g(4)

⇒ 64a + 45 = 108 + a

⇒ 64a – a = 108 – 45

⇒ 63a = 63

⇒ a =  6363  = 1

∴ The value of a is 1.