Can a quadratic equation aX^2 + bX + c = 0, where a, b, and c...
Can a quadratic equation aX^2 + bX + c = 0, where a, b, and c are rationals, has one rational solution and one irrational solution? Prove or disprove with justification.
Homework Answers
Let f(x) = ax^2 +bx +c be a quadratic whose coefficients a, b, c are rational....
Let f(x) = ax^2 +bx +c be a quadratic whose coefficients a, b, c are rational. Prove that if f(x) has one rational root, then the other root is also rational.
In Python. The two roots of a quadratic equation ax^2 + bx + c = 0...
In Python. 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 the quadratic equation ax**2 + bx + c = 0 Please solve this on...
1. Solve the quadratic equation ax**2 + bx + c = 0 Please solve this on python.
C++ The roots of the quadratic equation ax² + bx + c = 0, a ≠...
C++ The roots of the quadratic equation ax² + bx + c = 0, a ≠ 0 are given by the following formula: In this formula, the term b² - 4ac is called the discriminant. If b² - 4ac = 0, then the equation has a single (repeated) root. If b² - 4ac > 0, the equation has two real roots. If b² - 4ac < 0, the equation has two complex roots. Instructions Write a program that prompts the...
Recall the quadratic equation ax2 + bx + c = 0. Prove that there does not...
Recall the quadratic equation ax2 + bx + c = 0. Prove that there does not exist any integer solution to this equation if a, b, and c are all odd integers. (No integer solution means that there does not exist any integer x that satisfies the equation ax2 + bx + c = 0).
Java Programming Question 4 (10 points): Solutions for a quadratic equation ax(squared)+bx+c= 0. where a does...
Java Programming Question 4 (10 points): Solutions for a quadratic equation ax(squared)+bx+c= 0. where a does not equal zero are as follows. r1=( −b+√b(squared)−4ac)/2a r2=(−b−√b(squared)−4ac)/2a if b(squared)−4ac <0, equation doesn’t have real roots. If it is 0 there is one root(r1=r2). Write a Java program to read a,b and c from keyboard and find the roots, if they exist. Note: You need to have a method that takes 3 real values as arguments
Use Python Programming. Design a class named Quadratic Equation for a quadratic equation ax + bx+c...
Use Python Programming.
Design a class named Quadratic Equation for a quadratic equation ax + bx+c 0. The class contains: • The data fields a, b, and c that represent three coefficients. . An initializer for the arguments for a, b, and c. • Three getter methods for a, b, and c. • A method named get Discriminant() that returns the discriminant, which is b- 4ac The methods named getRoot 1() and getRoot 2() for returning the two roots of...
algebra 2 Solving the quadratic equation using the quadratic formula ax²+bx+c 01 x= -htb² - 4ac...
algebra 2 Solving the quadratic equation using the quadratic
formula
ax²+bx+c 01 x= -htb² - 4ac Ex3 - 2x² +3 x =4-15 X X - 2x²-x =-15 +15 +15 - 2x2-x+15= 0 A = -2 D- C= 15
for a matrix solution of the quadratic (3) Find a formula of the form x = -B C equation ax2 + bx +c = 0. Here c denotes...
for a matrix solution of the quadratic (3) Find a formula of the form x = -B C equation ax2 + bx +c = 0. Here c denotes and 0 denotes 0 0 (Hint: First show how the square root of any number D can be obtained using a where it looks different depending matrix of the form on whether D is negative. Then use the quadratic formula.) positive or
for a matrix solution of the quadratic (3) Find a...
The equation for a parabola has the form y=ax^2+bx+c, where a, b, and c are constants...
The equation for a parabola has the form y=ax^2+bx+c, where a, b, and c are constants and a≠0. Find an equation for the parabola that passes through the points (−1,0), (−2,−1), and (−6,15). Answer: y =
Use Python Programming.
Design a class named Quadratic Equation for a quadratic equation ax + bx+c 0. The class contains: • The data fields a, b, and c that represent three coefficients. . An initializer for the arguments for a, b, and c. • Three getter methods for a, b, and c. • A method named get Discriminant() that returns the discriminant, which is b- 4ac The methods named getRoot 1() and getRoot 2() for returning the two roots of...
algebra 2 Solving the quadratic equation using the quadratic
formula
ax²+bx+c 01 x= -htb² - 4ac Ex3 - 2x² +3 x =4-15 X X - 2x²-x =-15 +15 +15 - 2x2-x+15= 0 A = -2 D- C= 15
for a matrix solution of the quadratic (3) Find a formula of the form x = -B C equation ax2 + bx +c = 0. Here c denotes and 0 denotes 0 0 (Hint: First show how the square root of any number D can be obtained using a where it looks different depending matrix of the form on whether D is negative. Then use the quadratic formula.) positive or
for a matrix solution of the quadratic (3) Find a...
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