Answer:
The equation is y = 2x² + 7x + 5
Step-by-step explanation:
In the quadratic equation y = ax² + bx + c
∵ The sum of the roots is [tex]\frac{-7}{2}[/tex]
∵ The product of the roots is [tex]\frac{5}{2}[/tex]
→ By using the rules above
∴ [tex]\frac{-b}{a}[/tex] = [tex]\frac{-7}{2}[/tex]
∴ [tex]\frac{c}{a}[/tex] = [tex]\frac{5}{2}[/tex]
→ Compare between them
∴ a = 2
∴ -b = -7 ⇒ divide both sides by -1
∴ b = 7
∴ c = 5
∵ The form of the quadratic function is y = ax² + bx + c
→ Substitute the values of a, b, and c in it
∴ y = 2x² + 7x + 5
∴ The equation is y = 2x² + 7x + 5
