Question

Consider the equation 3x^2 + 5x + 2 = 0

a) Write the Cavtored form of the trinomial.
b) What are the roots of the equation?

Answer 1

Factored Form : (3x + 2)(x + 1)

Roots: x = -2/3, x = -1

Explanation:

Multiply 2 (the term with no variable) by 3 (coefficient of the first term with a degree of 2) to get 6

Use The Diamond Method See attachment

Factor :

• 3x² + 5x + 2
• 3x² + 3x + 2x + 2 (split 5x into 3x and 2x)
• 3x(x + 1) + 2(x + 1)
• (3x + 2)(x + 1)

Roots:

• (3x + 2)(x + 1) = 0

Using Zero-Product property:

• 3x + 2 = 0
• 3x = -2
• x = -2/3

Second scenario:

• x + 1 = 0
• x = -1

-Chetan K