Question

7. Give the formula of avoiding roundoff error to solve each of the fol- lowing problem and compute the numerical values. All the results are approximated to 4 digits with rounding arithmetic. (1). Find the roots of the quadratic equation 123 1 2+ 1 0 4 6 (Hint: first observe b and 62 - 4ac) -5+ b2 - 4ac c/a (Answer:21 22 = ; 21 = 92.24, 22 2a I 1 10-3) 5.420 x 9 (2). Compute In (50 – V2499 (Answer: In (x – V 22 - 1) = = - In (x+Vx2 - 1); -4.605) 4

Answer 1

#first one source code:

a=1/3;
b=-123/4;
c=1/6;
x1=(-b+sqrt(b^2-4*a*c))/(2*a);
x2=(c/a)/(x1);
fprintf("x1=%.4f\nx2=%.4f\n",x1,x2);

#outtput:

>> data xl=92.2446 X2=0.0054 >>|

#second one source code:

data=log(50-sqrt(2499));
printf("%.4f\n",data);

#output:

Command Window >> data -4.6051 >> |

#third one source code in matlab:

data=(exp(0.02)-exp(-0.02))/(0.03);
fprintf("%.4f\n",data);

#output:

>> data 1.3334 >> |

#forth one source code;

data=sqrt(100.01)-sqrt(99.99);
fprintf("%.4f\n",data);

#output:

Command Window >> data 0.0010 >> |

#by using matlab we can get the data all are 4 decimal places..