EXERCISE 15 The quadratic equation 3x2 + px + q = 0 has roots 2 and -3. Find: 1) The value of p and of q. 2) The range of the values of k such that 3x2 + px + q = -3k has no real roots.

Q: An isosceles triangle has a base 6 m in length and the unequal angle is 73.74°. Calculate, showing…

A: Let us solve the given geometry based problem in the next steps.

Q: Exercise #4: Consider the equation x-7 =-2 (a) Show that x=5 is not a solution to this equation. (b)…

A: here given  |x-7| = -2 answer (a) this function is defined differntky for values range of x when x…

Q: Two quadratic equations were solved using quadratic formula. Equation 1: 2a2 + 3 = 8x a = 2, b = -8,…

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: What are the solutions to the equation on [0, 27)? 2/3 csc (3x) 3 Drag all solutions to the box to…

A: We have to find solutions

Q: 1. Do you wholly agree with the statement that “the domain and range of a quadratic equation will be…

A: A quadratic equation is defined as ax2+bx+c=0 where a≠0, here a,b,c are arbitrary constants. Domain…

Q: Solve of AABC. 2. ABCD is a square of side 6 cm. If a rectangle of length (2x- 1) cm and width (x +…

A: Area

Q: Use the quadratic formula to solve for x. 2x-2x-1=0 (If there is more than one solution, separate…

A: The general quadratic equation is of the form ax2+bx+c=0, where a, b and c are the coefficients. The…

Q: 10. Write the sustem of lineor equations in the form Arebuand solve this motrit equat 2と, X, t Xu-9…

A: Given: 2x1  -x2 +x4 =93x2 -x3 -x4 =-9x1 +x3 -3x4 =-2x1 +x2 +2x3 =0 To find : x1x2x3x4 for system of…

Q: Practice question 27

A: Find the exact solution of the equation

Q: 1,5х + 2х, 3D 4 4x1 +X2 = 6

A:

Q: Write a quadratic equation having the given solutions. 11, 4. |%3D0 (Type an equation whose terms…

A:

Q: 11. Without solving, determine the number of real solutions for each quadratic equation. Show work.…

A: Given:- a) 5q²-3q-6=0 b) 3y²-5y +9=0  To find:- Number of real roots of given quadratic equations

Q: Write a quadratic equation in standard form with roots -7/3 and 2 passing through the point (0,28).…

A: Quadratic equations  with roots p,q  y=a(x-p)(x-q)  Standard form of quadratic equation y=ax2+bx+c

Q: Assume that P and Q are two positive distinct real roots of the quadratic equation (²₂. - -…

A: given quadratic equation t2-P+Qt+PQ=0 here assume that P and Q are two positive distinct roots of…

Q: Solve the equation with quadratic formula (with the work) 2x2 - 12x + 18 = 0 2p2 - 8p + 6 = 0 2n2…

A: As per guideline we have to solve only three subparts

Q: Use the quadratic formula to find a solution to 3 22 – 2z+6 = 0 22 Syntax hint: e.g. to enter 1 +…

A:

Q: Find the equation of a quadratic function that has the following root x = 5i and x = - 5i and passes…

A: We need to find the equation of a quadratic function that has the following root x = 5i and x = - 5i…

Q: (a) Show that the equation x6 – 5x – 5 = 0 has at least one solution on the interval [-1, 0).

A:

Q: write a quadratic equation with integer coefficients and the given numbers as soluitons (use x as…

A:

Q: What is the maximum number of real distinct roots that a quartic equation can have? a) infinitely…

A: ## we want to find out that how many real distinct roots that a quartic equation can have.

Q: Which of the following quadratic equations contains the vertex (-5, 6) and has a y-intercept of (0,…

A: Given: - The vertex of the quadratic equation is, (-5,6) and has a y-intercept of (0,31) To find: -…

Q: In examining the quadratic formula, explain in detail what is the discriminant of the formula and…

A:

Q: The model H described by H=2.75x +71.48 can be used to predict the height, in centimeters, of a…

A: Given data:     The given expression for the height of the woman is: H=2.75x+71.48. The length of…

Q: Do you wholly agree with the statement that “the domain and range of a quadratic equation will be…

A: step:-1 Statement:- The domain and range of a quadratic equation will be -∞,∞. 1. The domain of a…

Q: Show that the equation x – 15x + c = 0 has at most one root in the interval [-2, 2].

A: Given the function

Q: EXERCISE 13 Form a quadratic equation that has the roots m and 2m. Express the equation in the form…

A:

Q: 6. Show that the quadratic equation ax² + b – a = 0 (a± 0) has two distinct real roots.

A:

Q: Solve for all solutions to 2cos 2t = v3 %3D

A:

Q: Exercise 6.4.2 Give the solutions to the following quadratic equations having real coefficients. (b)…

A: We will find out the required solution.

Q: (4) Show that in general the sum of the roots of a quadratic equation ax? + bx +e=0 b is --whereas…

A: Let u and v be the roots of a quadratic equation ax2+bx+c=0. To obtain the equation from the roots,…

Q: 27. Find the exact solutions and simplify as much as possible: 3x = 6x + 2. Show work.

A:

Q: 5. Write a quadratic equation in standard form that has solutions of x = -6 and x = 7.

A: We have to write the quadratic equation in standard form that has solution of x = -6 and x = 7.

Q: Assume the least square equation is ŷ = 10+20X. What does the value of 10 in the equation indicate?

A: Given: least square equation  ŷ = 10+20X Value of 10 in equation = ?

Q: Show that the equation x3 - 17x + c = 0 has at most one root in the interval [-2, 2].

A:

Q: Exercise 3. Show that Equation (22) is indeed a solution of Equation (20). Verify that, taking po 1,…

A: To verify that  Pk=14+P0-14-115k; k≥0 For P0=1 satisfies  Pk+1=415-115Pk Put P0=1…

Q: Find the complete or particular solution of the following diffi- rential equations:

A:

Q: Exercises 25–28: Solve by completing the square. 25. x² + 2x = 5 26. x² - 3x = 3 27. 2:2 – 62 - 1 =…

A: “Since you have asked multiple question, we will solve the first question for you. If you  want any…

Q: 1. Which terms apply to the real solutions of a Quadratic equation? Choose all that apply. A)…

A: For solution, we equate the quadratic equation to zero and solve for x .

Q: 18. Choose the correct answer. Use the values of the vertex and point to choose the correct…

A:

Q: Write a quadratic equation with integer coefficients with no common factors, which has the given…

A:

Q: 4. Which of the qundratic equation has no real roots? 1. x*+ 3x - 10 -0 5 Whnt is the nature of…

A: The equation ax2 +bx+c= 0 has real roots if b2 -4ac=0

Q: 1. Use the worked example to write a quadratic equation that passes through.the points (-1, 5), (0,…

A:

Q: Present a quadratic equation in the form ax2 + bx + c = 0 where a > 1. •How many solutions does…

A: Here is the solution

Q: 2. Write an equation in standard form ax? + bx + c that has roots of x = 4,. %3D

A: The roots of given equation is x=4,12 To find the equation in standard form

Q: A two digit number is such that the product of the digits is 12.When 36 is added to the number the…

A: Here we want to find quadratic equation whose root is a digit on the required number. We use the…

Q: Find the equation, in vertex form, of the quadratic equation with zeros -1 and 7 and through the…

A: Given: The roots of the quadratic equation as -1 and 7 and the graph of quadratic equation is…

Q: List all the possible of methods of solving Quadratic Equation of the form: ax2 + bx + c

A:

Q: 3. If you could only learn one approach to solving quadratic equations, discuss which of the…

A: 3. If I could learn one approach to solve quadratic equation, I would learn the method of completing…