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Q: For which values of the constant a has the equation no real roots? X + In! a

A: The graph of the function a=x+ln1x is shown below.

Q: If the roots of the equation a(b - c)x² +b(c - a)x + c (a - b) = 2 11 are equal, show that ==±+:

A: We can use properties of square of three no. To solve the problem

Q: 1) Prove that there are no positive integer solutions to the equation x2-y?=1

A:

Q: Expand and simplify to express each equation in standard form. [2, 2, 2, 3, 3, 2] a) y = (x +5)(x +…

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve first three…

Q: Show that the product of the roots of a quadratic equation is c/a .

A: Consider the quadratic equation ax2+bx+c=0 Also consider that α and β are the roots of the quadratic…

Q: Find all 4 roots of the equation z4+1=0.

A: Concept:

Q: Зх + 1 = 4 – ex 2 – 4x

A: We Calculate the roots of the following equation using (i) Newton Rapson's Method (ii) Bisection…

Q: t Sintcost de

A:

Q: Explain Muller’s method to find a root of an equation. And give one illustrative example

A:

Q: Find all the values for the fifth root of z = 32

A: We have to find all the values for the fifth root of z=32.

Q: 3) Solve for x -2+ Va + 3 = -5

A:

Q: (15x - 8) 226

A: Given,

Q: Make an appropriate substitution and solve the equation √(3+√(x+√(x+1)) ) =2

A: In this question we will find the value of 'x'.

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.  

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.