Q.5. Find all roots of x-3x-230using Cardano's formula.

Q: 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…

A: Given mx2+x2-m+3=0        ...(i)

Q: Which of the following is not a 6-th root of unity that is not a solution to? z6 = 1 a. +i- b. -1 c.…

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Q: If y = C1 + C2x +e2*(C3cosx + C4sinx), then the roots are

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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: Find all solutions of the DE y"– 12 y '+36 y=16 te°* (where t is a real constant)

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

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

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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: Determine the re al roots of the equation fx) = 5x - 5x2+ 6x – 2 using iterations of the bise ction…

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Q: If L(x)=mx+b is the linearization of the cube root of 3x+1 at x=333, then b= Enter your answer as a…

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

A: Given z4+1=0

Q: 4. Find the distinct roots of z for the following equation, z4 = 3i.

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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 a, a2 an are the positive roots of Jo () = 0, show thet ..*** %3D ("D) !p "D/(x "D) °r3

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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: Find the 3 roots of the equation x3-1.25x+0.25 using BAIRSTOWS METHOD. USE r=1 amd s=2

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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: 16. The roots of the equation x+ 2px + q = Odiffer by 1. Show that p q - 4.

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

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: f(x) %3Dх3 — 5х? -2х + 10

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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

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

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Q: 4 Find the roots of Z'+1=0_ Hint s i -e t.

A: We have to find root of z^4+1=0

Q: • X1 – 5X2 + X3 = 9 • 2X1 – 3X2 + 2X3 – 12X4 = 5 X1 + 2X + 10Х3 + 3X4 15 %D |

A: Solving the system of linear equation by Gauss-Seidal method with initial guess (0,0,0,0)

Q: DETERMINE THE ROOTS OF THE EQUATION USING: REGULA FALSI METHOD f(x) = x - 3x + 1 %3D Lising a…

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Q: (2) By using the secant method, find an iterative formula to find the value of ym where m is a…

A: Here x2-5=0∴x2-5=0Let f(x)=x2-5Here x 0 1 2 3 f(x) -5 -4 -1 4 1st iteration :x0=2 and…

Q: Find the roots of the following equation x6 – x – 1 = 0 Using an initial guess of xo =1.5 ?

A: We have to find the roots of the given equation.

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)

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

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

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Q: Q 2- use Newton-Raphson method to obtain a root of equation x' - 2x + 3x -5 = 0

A: The given problem is to find the approximate root of given function using newton raphson method.…

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

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Q: find the differentiate of h(t)= the 5th square root of t - 5e to the power of t

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Q: 1 = + 3 3 Vx 3 y x

A: Given 1 = 23(x)1/3+ 13(x)2/3 Let's assume  t = x1/3   then t2 = x2/3  Substituting the values in the…

Q: Q3/ by using De Moivre's theorem find the third roots of 23 – 1 = iV3

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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: Q1/ Find the cubic root of Z = -i?

A: As per our guideline we are allowed to do 1 question at a time. Please post other questions next…

Q: Given that k#1 and the roots of the equation z' = k are à, B (x-2) and Y, use the substitution z =…

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Q: 15. Show that the equation, 2³ + e* = 0 has exactly one real root.

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Q: Ose the quadratic formola to solue for x. Ax+9x-1=D0 (If there is more than one solutiont seperate…

A: We need to solve the following quadratic equation 4x2+9x-1 = 0…

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: Solve the Following DE y-y-6y= 2sin X

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Q: nchon (he pe 1. x + 9x2 + 26x + 24 = 0 a. Good guesses: b. # of positive roots: c. # of negative…

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Q: 2. Solve the following equation for t using the quadratic formula: at2 S= vt + -

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Q: ve the following equation for æ. Express your answer in the

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Q: (D² + 1)y = sec? x csc x

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Q: 5. Determine the root(s) for the following equation: 3x +5 = 10x

A: We have to find roots

Roots

The main dissimilarity between real and complex roots is that the real roots are obtained as real numbers, in contrast with the complex roots, which are indicated as imaginary numbers. The standard format for depicting any complex number is in the form of a + bi.