Answer:
Answer is 2x^2-23x+45=0.
Step-by-step explanation:
x1=5/2 and x2=9
x1+x2=-b/a
x1*x2=c/a
ax^2+bx+c=0 /:a
x^2 +(b/a)x+c/a=0
x^2 - (x1+x2)x+x1 *x2 =0
x^2 - (5/2+9)x+(5/2)*9=0
x^2 - (5/2+18/2)x+45/2=0
x^2 - 23/2x+45/2=0 /*2
2x^2-23x+45=0
Answer:
2x² - 23x + 45 = 0
Step-by-step explanation:
Given the roots of the quadratic are x = [tex]\frac{5}{2}[/tex] and x = 9
Then the factors are (x - 9) and (x - [tex]\frac{5}{2}[/tex] )
The quadratic equation is then the product of the factors, that is
(x - 9)(x - [tex]\frac{5}{2}[/tex] ) = 0 ← expand the factors using FOIL
x² - [tex]\frac{5}{2}[/tex] x - 9x + [tex]\frac{45}{2}[/tex] = 0, that is
x² - [tex]\frac{23}{2}[/tex] x + [tex]\frac{45}{2}[/tex] = 0
Multiply through by 2 to clear the fractions
2x² - 23x + 45 = 0
