Write a quadratic equation with the given roots. Write the equation in the form , where a, b, and c are integers.5/2 and 9
2x2 – 23x + 45 = 0

2x2 + 23x – 45 = 0

x2 – 23x + 45 = 0

x2 – 23x – 45 = 0
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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

2x² - 23x + 45 = 0

Step-by-step explanation:

Given the roots of the quadratic are x = and x = 9

Then the factors are (x - 9) and (x - )

The quadratic equation is then the product of the factors, that is

(x - 9)(x - ) = 0 ← expand the factors using FOIL

x² - x - 9x + = 0, that is

x² - x + = 0

Multiply through by 2 to clear the fractions

2x² - 23x + 45 = 0

the answer is b