Write a quadratic equation with roots of 1/3 and −7/2.
Accepted Solution
A:
Answer: Quadratic equation with roots 1/3 and -7/2 is:[tex]6x^{2} + 19x - 7 = 0[/tex]Step-by-step explanation:Roots of the equation are 1/3 and -7/2Quadratic equation is of the form:[tex]ax^{2} +bx + c = o[/tex]Now Sum of roots = [tex]\frac{-b}{a}[/tex]Sum of roots = [tex]\frac{1}{3} + (\frac{-7}{2}) = \frac{2 - 21}{6} = \frac{- 19}{6} = \frac{- b}{a}[/tex]∴ b = 19 and a = 6Product of roots = c/aProduct of the roots = [tex]\frac{1}{3} \times \frac{-7}{2} = \frac{-7}{6} = \frac{c}{a}[/tex]∴ a = 6, b = 19 and c = -7So the quadratic equation with roots 1/3 and -7/2 is:[tex]6x^{2} + 19x - 7 = 0[/tex]