Question

The expressions x² + bx + 10 and (x - 3)2 +c,

where b and c are constants, are equivalent. What is
the value of b + c ?

Answer 1

7

Explanation:

`x^2 + bx + 10 = (x-3)^2 + c\\x^2 + bx + 10 = (x-3)(x-3)+c\\x^2 + bx + 10 = x^2 - 6x + 9+c\\`

if two equations are equivalent, that means that each coefficient is the same

meaning that.

`bx = 6x\\and\\10 = 9 + c\\so\\b = 6\\and\\c = 1`

Note that 10 is the coefficient of
`x^0`

so, b + c = 6 + 1 = 7