Answer:
[tex]\large \boxed{\sf \ \ \ (x+2)(x-\dfrac{1}{2}) \ \ \ }[/tex]
Step-by-step explanation:
Hello,
let's solve
[tex]x^2+\dfrac{3}{2}x-1=0\\\\<=> 2x^2+3x-2=0 \ \text{multiply by 2}\\\\\\[/tex]
[tex]\Delta=b^2-4ac=9+4*2*2=9+16=25[/tex]
There are two solutions
[tex]x_1=\dfrac{-3-\sqrt{25}}{4}\\\\x_1=\dfrac{-3-5}{4}\\\\x_1=\dfrac{-8}{4}\\\\\boxed{x_1=-2}[/tex]
And
[tex]x_2=\dfrac{-3+\sqrt{25}}{4}\\\\x_2=\dfrac{-3+5}{4}\\\\x_2=\dfrac{2}{4}\\\\\boxed{x_2=\dfrac{1}{2}}[/tex]
So we can write
[tex]x^2+\dfrac{3}{2}x-1\\\\=(x-x_1)(x-x_2)\\\\=(x+2)(x-\dfrac{1}{2})[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
