Question

Given r_1 and r_2 are the roots of the quadratic equation ax^2 + bx + c = 0,

express (b^2?4ac)/2a in terms of r_1 and r_2. Re-write the quadratic formula in terms of r_1 + r_2 and

and r_1 ? r_2.

Answer #1

Write a C++ programming code for a non-zero,
discuss the roots of the quadratic equation as follows:
a) D =0; the equation has a double solution.
x1 = x2 = -b/2a
b) D>0; the question has two different solutions x1 and
x2.
x1= (-b-sqrt(D))/2a
x2= (-b+sqrt(D))/2a
c) if D<0; the equation has no real solution

Suppose that f(x)=ax^3+bx^2+cx+d cubic polynomial.. Show that
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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.

Let
a, b and c be real numbers with a does not equal to 0 and
b^2<4ac. Show that the two roots ax^2+ bx + c =0 are complex
conjugates of each other.

1) Solve the given quadratic equation by using
Completing the Square procedure and by
Quadratic formula ( you must do it both ways).
Show all steps for each method and put your answer in simplest
radical form possible.
4X2 + 4X = 5
2) Which part of the Quadratic Formula can help you to find the
Nature of the roots for the Quadratic Equation. Explain how you can
find the nature of the roots and provide one Example for...

Find the roots of the quadratic equation, 3x^2-x=14.

quadratic function is a function of the form
y=ax2+bx+c where a, b, and c are constants. Given any 3
points in the plane, there is exactly one quadratic function whose
graph contains these points.
Find the quadratic function whose graph contains the points (5,
45), (−3, 5), and (0, 5).
Enter the equation below.

Given the components of the vectors, A, B, and C
Ax = 5 Bx=4 Cx =10
Ay = -3 By=6 Cy =6
Az = 10 Bz=-2 Cz =0
Find (a) AiCiBx, (b) AiAyBi, (c) AiBiCj , and (d) AiBiCjAk

Discuss the possible loss-of-significance error that may be
encountered in solving the quadratic equation
ax2+bx+c=0. How might that loss-of-significance error be
avoided?(You only need to discuss one case).

Let A be a given (3 × 3) matrix, and consider the equation Ax =
c, with c = [1 0 − 1 ]T . Suppose that the two vectors
x1 =[ 1 2 3]T and x2 =[ 3 2 1] T are
solutions to the above equation.
(a) Find a vector v in N (A).
(b) Using the result in part (a), find another solution to the
equation Ax = c.
(c) With the given information, what are the...

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