Answer:
2x² + 7x + 3 = 0
Step-by-step explanation:
[tex]\sf \text{Sum = -3 + $(\dfrac{-1}{2})$}[/tex]
[tex]\sf = \dfrac{-3*2}{1*2}-\dfrac{1}{2}\\\\=\dfrac{-6}{2}-\dfrac{-1}{2}\\\\=\dfrac{-7}{2}[/tex]
[tex]\sf \text{Product =$-3*\dfrac{-1}{2}$}[/tex]
[tex]= \dfrac{3}{2}[/tex]
Quadratic polynomial:
[tex]\boxed{x^{2}-sum *x+product = 0}[/tex]
[tex]x^{2}- \left(\dfrac{-7}{2}\right)x+\dfrac{3}{2}=0\\\\x^{2} + \left(\dfrac{7}{2}\right)x+\dfrac{3}{2}=0\\[/tex]
Multiply the entire equation by 2
[tex]2*x^{2} + 2*\dfrac{7}{2}x +2*\dfrac{3}{2}=0[/tex]
2x² + 7x + 3 = 0
