Let p and q be the two roots of the equation mx? +x(2-m)+3=0. 2 Let m,, m, be the values of m satisfying 3 m, Determine the numerical value of m2

Q: Given that a, B and y are the roots of the equation 423 – 522 + 3z + 11 = 0. a3 Without finding a, B…

A:

Q: 03: Using False-Position Method, find the Root of the following equation: e* – 3. x² = 0 , for the…

A:

Q: Which of these equations has two real roots: Select one: O a. x2-4x + 4 =0 O b. x2 - 10x + 100 = 0 O…

A:

Q: Find all the roots of z for the following equation (2 – j6) z + (3+ j5) z – 5 + j = 0 -

A: Given is a quadratic equation, we use the quadratic formula for finding the roots. Also we use the…

Q: m = -3, -2+i,

A:

Q: Explain why the following five statements ask for the same infor-mation. a. Find the roots of ƒ(x) =…

A:

Q: Given p(x)=x -3 and &, =0.01. %3D a) Obtain the root of p(x) using False Position and Bisection…

A:

Q: What is/are the value/s of k if the roots of X2 + x + k = 4 are equal?

A:

Q: Ex:. Find the fourth roots of Z=-di Say no 4 K = 0₁12₂3

A: given z=-8i To find the fourth root of the given complex number proceed as follows comparing the…

Q: 4 Find the roots of Z²+1=0 itt/2 Hint i = e 3

A: Given z4+1=0

Q: 4. If A is the set of roots of the equation x³ – 3x + 2 = 0, then A is equal to a) {1; –3; 2} b)…

A: We have to find the roots of the given equation. To find roots of this equation we are going to…

Q: B. Give the general solution to the HLDE with the given set of auxiliary roots 3. m = -3, -2±i, l±2i

A:

Q: The positive root of x +2x-2=0, by Newton-Raphson method, correct upto three significant figures is…

A: Let fx=x2+2x-2⇒f'x=2x+2Now put x=0 we get     f0=-2Again put x-1  we get     fx=1+2-2=1⇒f0=-2<0…

Q: If pq > 0 and the roots of (x' + mx + m = 0 are in the ratio p:q then equals (a) 1 (b) 0 (c) (d)

A: We know, lx2+mx+m = 0Let,p, q be the roots of the quadratic equationwe know that,1. p+q = -ml2. pq =…

Q: refer to the given: (D* + 6D: + 9)y = 0 Solve for the roots: +/- V2i , +/- VZi +/- V4i , +/- V4i A.…

A:

Q: You are given a quadratic equation of the form (x – p)(x – q) = 0. Show that the axis of symmetry of…

A:

Q: Which of the following is the complete set of roots of the auxiliary equation fory""-3y+3y'-y = 0.

A: Given y'''-3y''+3y'-y=0

Q: Solve the following quadratic equation for all values of x in simplest form. 2(x + 10)2 – 37 = 13…

A: We need to solve this Quadratic equation

Q: a- Employ the Newton-Raphson method to determine a real root for initial guesses of 4.52 for…

A: Given equation, fx=-1+5.5x-4x2+0.5x3 To find the real root using Newton-Raphson method for initial…

Q: Use the False Position method of finding roots of equations to solve the following:…

A: Consider the given function, fn=40n1.5-875n+35000=0 Find the value the function, n 50 55 60 62 63…

Q: l roots

A: .

Q: B) Find the approximate roots of the following equation: f (x) = x³ – 8 = 0, on the closed interval…

A: Use the bisection method to find the roots of x3-8=0 find two points such that f(a)fb<0…

Q: If p(q=r) prove that x +q{r-p}x+p-q) = 0 has equal roots, ther 211 q = р

A:

Q: Which of the following is the complete set of roots of the auxiliary equation fory"'' - 3y "' + 3y…

A:

Q: What is one root of this equation? 2x2 – 4x + 9 = 0 %3D -2 + 14, O B. -1 + , O A. O c. 1+ 14, OD.…

A:

Q: Use the Newton-Raphson method of finding roots of equations to solve the following: where a = 2.5. 1…

A: The Newton-Raphson method (also known as Newton's method) is a way to quickly find a good…

Q: Find all the roots of z = -4 + (4V3)i giving each root in the form re". %3D 8° = -4+ (43) C

A:

Q: fa,b.c are in HP and a.B are the roots of ax + bx +c = 0. Fhen prove that the HM of a.B is (1+ aß)

A:

Q: 59. Let a, c +0. Show that the roots of ax? + bx +c = 0 cx? + bx + a =0 and are reciprocals of each…

A:

Q: Use the intermeiate value theorem to show that the following equations has at least two distinct…

A: Solved below

Q: obtain the four roots of characteristic equation as follows: p+ Vp? – 8pi? 272 p- Vp? - 8pi? 212 12…

A: As per the instruction, we will have to find the roots that are marked in blue. So, we will be…

Q: Find all the roots of z for the following equation (-5+ j4) z² + (3 – j5) z + 4 + j3 = 0

A: In order to find the roots of z we must apply the formula of roots of quadratic equation as the…

Q: Find the two roots of the quadratic function f(x) = 9x? – 3 – 1 Enter your answers as exact…

A: We will solve the problem

Q: 6. Determine the four roots of the equation (z–2)*+(z+1)' = 0 and plot them on an Argand diagram.

A:

Q: Given that P(z-M)-0 wherei(1LO(1-20andP and Q are real constants. Write down in a form a+bi and find…

A:

Q: (1– (C+D)), provided (C+D) 4PQ. (28) Substituting (25) and (26) into (28), we get the condition…

A:

Q: Find the formula, in standard form y=ax^2+bx+c, for a quadratic that has roots at x = -7 and x = 9,…

A: our objective is to find  the formula, in standard form y=ax^2+bx+c, for a quadratic that has roots…

Q: If plq-r)x+q (-p)x+rp-q) = 0 has equal roots, then prove that ² = 1,1 9 Pr pr

A:

Q: Solve z+z +1= 0 by obtaining the roots. Answer a. b(1+jv3), }(-1± N) 幸 d. (1+ jv/3), (-1±jv3)

A:

Q: Evaluate all the roots of the equation: z* +1 = 0

A: Given equation is z4+1=0. We have to evaluate the all roots of the given equation. Subtract 1 from…

Q: Solve the following equations in Z, with x expressed in both standard and non-standard names: (i) xx…

A:

Q: Let r, r; and r, be the roots of x' + 3x + 2 = 0, construct the equation whose roots are: :Select…

A:

Q: Let A and B be real numbers such that a root of the equation z ^ 3 + Az ^ 2 + Bz + 26 = 0 is 1 + i.…

A: First of all, as coefficients A and B are real, we know that, if z ∈ C is a root of an equation,…

Q: What are the values (roots) for lambda if alpha and beta are constants?

A: According to the given information, it is required to calculate the roots of the given equation:

Q: 8. Which of the following are approximate roots of the equation -óx? + 20 = 43x? a x--7.61, 0.44 c…

A:

Q: If a, b are the roots of x2 + px + 1 = 0 and c, d are the roots а, of x? + qx + 1 = 0, then the…

A: Introduction :

Q: The root of which of the following equations is most appropriate to approximate 2-1 O V2x-2=0…

A:

Q: (D² + 1)y = sec? x csc x

A:

Q: . Given that z = 1 is a root, find the other two roots of 2z3 −z2 +3z−4=0

A:

Q: 1? Which of the following quadratic functions has roots x = 3 and x = O x?+ 4x + 3 O x? + 2x – 3 O…

A:

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: