If f (x) = 5x^2-3 and f (x+a) = 5x^2+30x+42, what is the value of a?

Answer:a=3

Step-by-step explanation:

f (x) = 5x²-3

f (x+a) = 5 (x+a) ²-3

Expanding RHS

5 (x+a) (x+a) - 3

5 (x²+2ax+a²) - 3

Open the bracket

5x²+10ax+5a²-3

Hence

f (x+a) = 5x²+10ax+5a²-3

Compare with

5x²+30x+42

10ax=30x

10a=30

a=3