Question

If `[(–1,–2,5),(–2,a,–1),(0,4,2a)]` = –86, then the sum of all possible values of a is ______. 

Options

• 4

• 5

• –4

• 9

Answer 1

If `[(–1,–2,5),(–2,a,–1),(0,4,2a)]` = –86, then the sum of all possible values of a is –4. 

Explanation:

`[(–1,–2,5),(–2,a,–1),(0,4,2a)]`

= –1 (2a² + 4) + 2 (– 4a + 0) + (– 8 – 0) 

= –86

–2a² – 4 – 8a – 40 = –86

–2a² – 8a = –86 + 44

–2a² – 8a = –42

2a² + 8a = 42

a² + 4a – 21 = 0

a² + 7a – 3a – 21 = 0

a(a + 7) –3(a + 7) = 0

a + 7 = 0 or a – 3 = 0

a = –7 or a = 3

= –7 + 3 

= –4