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diff --git a/29/CH7/EX7.24.11/exa7_24_11.sce b/29/CH7/EX7.24.11/exa7_24_11.sce
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+//caption:root_locus
+//example 7.24.11
+//page 308
+clc;
+s=%s;
+syms K
+clf();
+g=K*(s+0.1)/(s*(s-0.2)*(s^2+s+0.6));
+Z=2
+P=2
+disp("the characterstics eq. is determined as:")
+CH=(s*(s-0.2)*(s^2+s+0.6))+K*(s+0.1)
+CH=sym('(s*(s-0.2)*(s^2+s+0.6))+K*(s+0.1)');
+disp('=0',CH,"characterstics_eq,CH=")
+eq=(s*(s-0.2)*(s^2+s+0.6))
+p=roots(eq)
+disp(p,"open loop poles are:")
+c0=coeffs(CH,'s',0);
+c1=coeffs(CH,'s',1);
+c2=coeffs(CH,'s',2);
+c3=coeffs(CH,'s',3);
+c4=coeffs(CH,'s',4);
+b=[c0 c1 c2 c3 c4 ]
+routh=[b([5,3,1]);b([4,2]),0]
+routh=[routh;-det(routh(1:2,1:2))/routh(2,1),routh(1,3),0]
+routh(3,1)=simple(routh(3,1))
+t=routh(2:3,1:2)
+l=simple(-det(t)/t(2,1))
+routh=[routh;l,0,0]
+routh=[routh;K,0,0]
+K=sym('-(s*(s-0.2)*(s^2+s+0.6))/(s+0.1)')
+d=diff(K,s)
+e=3*s^4+2*s^3+0.64*s^2+0.08*s-0.12
+r=roots(e);
+disp(r,"r=")
+disp("since -0.37 and 0.08 lies on root locus, so the breakaway point is -0.37 and 0.08 ")
+disp(routh,"routh=")
+disp("for given system to be marginally stable:");
+disp("(625*K^2-310*K+33)/(625*K-275)=0 ");
+disp("which gives:");
+disp("K=0.148 and 0.352");
+K1=0.148;
+K2=0.352
+a=((11-25*K1)/20)*s^2+K1/10//intersection of root locus with jw axis
+r1=roots(a)
+b=((11-25*K2)/20)*s^2+K2/10//intersection of root locus with jw axis
+r2=roots(b)
+disp(r1,r2,"root locus crosses imaginary axis at:")
+g=(s+0.1)/(s*(s-0.2)*(s^2+s+0.6));
+G=syslin('c',g)
+evans(G,200)
+xgrid(2)
+v=[-1 0.7 -2 2];
+mtlb_axis(v)
+\ No newline at end of file