If the mean and the standard deviation of the data 3,5,7,a,b are 5 and 2 respectively, then a and b are the roots of the equation:

Given that the mean of the data is 5,⇒3+5+7+a+b5=5⇒a+b=10The standard deviation is 2, the variance is 4          Hence,9+25+49+a2+b25−52=4⇒a2+b2=62 By solving the above two equations ab=19 Therefore, the equation whose roots are a,b is x2-10x+19=0