1) = -7f(2) = 16Therefore, root lies between 1 and 2a = 1; f(a) = -7b = 2; f(b) = 16Substituting the values in the formula,X = \(\frac{bf(a)-af(b)}{f(a)-f(b)}\),we get \(x1 = \frac{2(-7)-16}{-7-16}\)=1.304347826; f(x1) = -1.334757952Therefore, x1 becomes a to find the NEXT point.\(X2 =\frac{2(-1.334757952)-(1.304347826)16}{-1.334757952-16}\)= 1.357912305; f(x2) = -0.229135731Therefore, x2 becomes a to find the next point.\(X3 = \frac{2(-0.229135731)-(1.357912305)16}{-0.229135731-16}\)=1.366977805; f(x3) = -0.038591868Therefore, x3 becomes a to find the next point.\(X4 = \frac{2(-0.038591868)-16(1.366977805)}{-0.038591868-16}\)=1.368500975; f(x4) = -6.478731338*10-3Therefore, x4 becomes a to find the next point.\(X5 =\frac{2(-6.478731338*10^{-3})-16(1.368500975)}{(-6.478731338*10^{-3})-16}\)= 1.368756579; f(x5) = -1.087052822 * 10-3Therefore x5 becomes a to find the next point.\(X6 = \frac{2(-1.087052822*10^{-3})-16(1.368756579)}{(-1.087052822*10^{-3})-16}\)=1.368799463; f(x6) = -1.823661977*10-4Therefore x6 becomes a to find the next point.\(X7 = \frac{2(-1.823661977*10^{-4})-16(1.368799463)}{(-1.823661977*10^{-4})-16}\)=1.368806657; f(x7) = -3.0601008*10-5Therefore x7 becomes a to find the next point.\(X8 = \frac{2(-3.0601008*10^{-5})-1.368806657(16)}{(-3.0601008*10^{-5})-16}\)=1.368807864.Therefore, the positive root corrected to 4 decimal places is 1.3688.