Question

solve equation x2+5x+6​

Answer 1

${x}^{2} + 5x + 6 \\ = {x}^{2} + (2 + 3)x + 6 \\ = {x}^{2} + 2x + 3 x + 6 \\ = x(x + 2) + 3(x + 2) \\ = (x + 2)(x + 3) \\ x = - 2 \: \: \: and \: \: \: x = - 3$

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Answer 2

Answer:

x = - 3, - 2

Step-by-step explanation:

Given : p(x) = x² + 5x + 6

On comparing this with ax² + bx + c, we get

a = 1, b = 5, c = 6

Using Middle Term Factorisation, we get

→ x² + 2x + 3x + 6

Taking out common terms, we get

→ x(x + 2) + 3(x + 2)

→ (x + 3)(x + 2)

For finding zeroes, factors should be equal to 0.

Using zero product rule.

→ (x + 3) = 0 and (x + 2) = 0

→ x = - 3 and x = - 2

• In Middle Term Factorisation, we factorise the middle term only.
• First we multiply 'a' and 'c'.
• Then we have to find such a pair of number such that on addition or subtraction, the result equals to 'b' and on multiplication, the result equals to the multiplication of 'a' and 'c'.

We get the two terms : 2 and 3

Addition = (3) + (2) = 5 = b

Multiplication = (3)(2) = 6 = Product of 'a' and 'c' i.e. (1)(6) = 6