1). Consider the quadratic equation x^2+ 100 x + 1 = 0 (i) Compute approximate roots...

1). Consider the quadratic equation
x^2+ 100 x + 1 = 0
(i) Compute approximate roots by solving
x^2 -100 x = 0
(ii) Use the quadratic formula to compute the roots of equation
(iii) Repeat the computation of the roots but use 3 digit precision.
(iv) Compute the relative absolute errors in the two 3 digit precision root approximations in (iii).
(v) With x1 =1/2a (-b + sqrt b^2 - 4ac and x2 = 1/2a (-b + sqrt b^2 - 4a, show that x1x2 =c/a and Discuss
the conditions under which one of the zeros can be trusted and the other zero not.
(vi) Using your 3 digit precision computations, recompute the second zero by rearranging x1x2 = c/a appromately

Expert Solution

Colby Messinger answered 1 year ago

use Java The two roots of a quadratic equation ax^2 + bx + c = 0...

use Java The two roots of a quadratic equation ax^2 + bx + c = 0 can be obtained using the following formula: r1 = (-b + sqrt(b^2 - 4ac)) / (2a) and r2 = (-b - sqrt(b^2 - 4ac)) / (2a) b^2 - 4ac is called the discriminant of the quadratic equation. If it is positive, the equation has two real roots. If it is zero, the equation has one root. If it is negative, the equation has no...

1. Solve quadratic equation Ax^2+Bx+C=0 using the quadratic formula x = (-B+ and - sqrt(B^2-4ac)) /...

1. Solve quadratic equation Ax^2+Bx+C=0 using the quadratic formula x = (-B+ and - sqrt(B^2-4ac)) / 2a) and output the two solution with clear explanation could you please do it in MATLAB

1. The equation 8?2 − 3?? = 0 has three roots. Find: (i) The first root,...

1. The equation 8?2 − 3?? = 0 has three roots. Find: (i) The first root, which is between -1 and 0, by the bisection method; (ii) The second root, which is between 1 and 2, by Newton’s method; (iii) The third root, which is between 3 and 4, by both the bisection method and Newton’s method. All the answers should be correct to 2 decimal places.

Consider the differential equation x′=[2 4 -2 −2], with x(0)=[1 1] Solve the differential equation where...

Consider the differential equation x′=[2 4 -2 −2], with x(0)=[1 1] Solve the differential equation where x=[x(t)y(t)]. x(t)= y(t)= please be as clear as possible especially when solving for c1 and c2 that's the part i need help the most

Write a program usingif-elseif-else statements to calculate the real roots of a quadratic equation ax^2+bx+c=0

Consider the the differential equation 2xy''+ 5y'+xy= 0 1) determine the indicial equation and its roots...

Consider the the differential equation 2xy''+ 5y'+xy= 0 1) determine the indicial equation and its roots 2) For each root of the indicial equation, determine the recurrence relation 3) Do the indicial roots differ by an integer? If yes, find the general solution on (0,∞). If not, find the series solution corresponding to the larger root on (0,∞)

Consider the differential equation (x 2 + 1)y ′′ − 4xy′ + 6y = 0. (a)...

Consider the differential equation (x 2 + 1)y ′′ − 4xy′ + 6y = 0. (a) Determine all singular points and find a minimum value for the radius of convergence of a power series solution about x0 = 0. (b) Use a power series expansion y(x) = ∑∞ n=0 anx n about the ordinary point x0 = 0, to find a general solution to the above differential equation, showing all necessary steps including the following: (i) recurrence relation; (ii) determination...

Write a program to input the coefficients of a quadratic equation and solve roots for all...

Write a program to input the coefficients of a quadratic equation and solve roots for all cases (including complex roots). VBA. x=(b ^2) - (4ac) I have it for 2 complex and 2 real and repeated. Is that all cases?

Find Roots of a Quadratic Equation Step 1: Analyze the Problem Accept three coefficients a, b,...

Find Roots of a Quadratic Equation Step 1: Analyze the Problem Accept three coefficients a, b, and c (all of data type double) of a quadratic equation: ax2+bx+c=0 Output real roots (double) of the equation Step 2: Develop a Solution Check for degenerate case (user enters 0 for both a and b), no solution Check if the equation is linear (user enters 0 for a), x = -c/b Calculate the discriminant = b2-4ac (obviously, the data type will be double)...

Consider the equation: ?̇ +2? = ?(?) with initial condition x(0) = 2 (a) If u(t)...

Consider the equation: ?̇ +2? = ?(?) with initial condition x(0) = 2 (a) If u(t) = 0, find the solution ?(?). What is ?(?) as t -> ∞? (b) If u(t) = 4+t, find the solution ?(?). What is ?(?) as t -> ∞? (c) If u(t) = ?3?, find the solution ?(?). What is ?(?) as t -> ∞? (d) If u(t) = δ(t), find the solution ?(?). What is ?(?) as t -> ∞?

Question