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If the expression (lx2 + mx + n) is equal to -4 when x = 0, it leaves reminder 5, when divided by (x - 3) and a reminder 3, when divided by (x + 1), then find the value of (l + m + n).

If the expression (lx2 + mx + n) is equal to -4 when x = 0, it leaves reminder 5, when divided by (x - 3) and a reminder 3, when divided by (x + 1), then find the value of (l + m + n). Correct Answer -6

lx2 + mx + n = -4 at x = 0

Putting x = 0:

⇒ n = -4

The expression leaves reminder 5 when divided by (x - 3);

∴ Putting x = 3 in the expression:

⇒ 9l + 3m - 4 = 5

⇒ 9l + 3m = 9

⇒ 3l + m = 3      ----(1)

The expression leaves reminder 3 when divided by (x + 1);

∴ Putting x = -1 in the expression:

⇒ l - m - 4 = 3

⇒ l - m = 7      ----(2)

From equation (1) and (2)

l = 10/4, m = -18/4 and n = -4

∴ (l + m + n) = 10/4 - 18/4 - 4 = -6

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