Answer:
(- 1.5, 1.5 )
Step-by-step explanation:
y = 4x² + 13x + 12 → (1)
y = x + 3 → (2)
At the point of intersection the equations are equal, that is
4x² + 13x + 12 = x + 3 ( subtract x + 3 from both sides )
4x² + 12x + 9 = 0 ← in standard form
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 4 × 9 = 36 and sum = 12
The factors are + 6 and + 6
Use these factors to split the x- term
4x² + 6x + 6x + 9 = 0 ( factor first/second and third/fourth terms )
2x(2x + 3) + 3(2x + 3) = 0 ← factor out (2x + 3) from each term
(2x + 3)(2x + 3) = 0 ← in factored form , that is
(2x + 3)² = 0 , then
2x + 3 = 0 ⇒ 2x = - 3 ⇒ x = - [tex]\frac{3}{2}[/tex] = - 1.5
Substitute x = - 1.5 into (2)
y = - 1.5 + 3 = 1.5
Thus there is only 1 point of intersection at (- 1.5, 1.5 )
