The difference between the roots of the equation 2x^2−5x+c=0 is 0.25. Find c.
Accepted Solution
A:
Answer:[tex]c=\frac{99}{32}[/tex]Step-by-step explanation:The given quadratic equation is [tex]2x^2-5x+c=0[/tex].Comparing this equation to: [tex]ax^2+bx+c=0[/tex], we have a=2,b=-5.Where: [tex]x_1+x_2=\frac{5}{2}[/tex] and [tex]x_1x_2=\frac{c}{2}[/tex]The difference in roots is given by:[tex]x_2-x_1=\sqrt{(x_1+x_2)^2-4x_1x_2}[/tex][tex]\implies 0.25=\sqrt{(2.5)^2-4(\frac{c}{2})}[/tex][tex]\implies 0.25^2=6.25-2c[/tex][tex]\implies 0.0625-6.25=-2c[/tex][tex]\implies -6.1875=-2c[/tex]Divide both sides by -2[tex]c=\frac{99}{32}[/tex]