Respuesta :
Answer:
see explanation
Step-by-step explanation:
Given 2x² + 5x - 12 in factored form, then to find the roots equate to zero, that is
(2x- 3)(x + 4) = 0
Equate each factor to zero and solve for x
2x - 3 = 0 ⇒ 2x = 3 ⇒ x = [tex]\frac{3}{2}[/tex]
x + 4 = 0 ⇒ x = - 4
Roots are x = - 4 and x = [tex]\frac{3}{2}[/tex]
Answer:
The equation (2x-3)(x+4)=0 should be solved to find the roots of 2x²+5x-12=0.
Step-by-step explanation:
The given equation is
[tex]2x^2+5x-12=(2x-3)(x+4)[/tex] .... (1)
We need to find an equation that should be solved to find the roots of the equation
[tex]2x^2+5x-12=0[/tex]
To find the roots of the equation we need to write the equation in factor form.
From equation (1) it is clear that the factor form of 2x²+5x-12 is (2x-3)(x+4). So using (1), we get
[tex](2x-3)(x+4)=0[/tex]
Using zero product property, we get
[tex](2x-3)=0\Rightarrow x=\frac{3}{2}[/tex]
[tex](x+4)=0\Rightarrow x=-4[/tex]
Therefore the equation (2x-3)(x+4)=0 should be solved to find the roots of 2x²+5x-12=0.
