The value of the coefficient b is - 43 and other root of quadratic equation is [tex]\frac{3}{5}[/tex]
The root of any equation is always satisfied that equation.
Since, root of equation [tex]5x^2+bx+24=0[/tex] is 8 .
So, [tex]5(8)^{2}+8b+24=0\\\\320+8b+24=0\\\\8b=-344\\\\b=-\frac{344}{8}=-43[/tex]
Now, equation become,
[tex]5x^2-43x+24=0\\\\5x^{2} -40x-3x+24=0\\\\5x(x-8)-3(x-8)=0\\\\(5x-3)(x-8)=0\\\\x=\frac{3}{5} ,x=8[/tex]
Therefore, the value of the coefficient b is - 43 and other root of quadratic equation is 3/5.
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