2. Let r, 2 be the roots of the equation 2x-6x+3=0, construct an equation whose roots and are rr3, zk and rr..

Q: Which of the following will simplify to the correct solutions for the equation 3z2 + z- 4=0?

A: correct answer is a  x=−b±√b2−4ac/2a where b=1 a= 3 c=-4

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

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Q: a. Show that If 1 iv3 z = 2 2 Then z7 = z. b. Evaluate all the roots of the Equation: z* + 16 = 0

A: We will solve both the parts only using some basic knowledge of complex numbers and their…

Q: Find an equation for each line in the form ax + by = c, where a, b, and c are integers with no…

A: Given: The required line is perpendicular to the line 2x-3y=5.

Q: If the roots of the equation x - 8x + a² - 6a = distinct, then find all possible values of a.

A: Since the roots of the given equation are real and distinct, We must have…

Q: Determine all the roots of R(y)=12y²+11y-5

A: R(y)=12y²+11y-5

Q: Which of the following quadratic equations has roots at (-4, 0) and (10, 0) and goes through the…

A: Option (C) is correct option. The roots of the equation are -4,0 and 10,0. So, x=-4,10. Use the…

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: If the roots of the equation a(b - c)x² +b(c - a)x + c (a - b)=0 2 _ 1 ,1. are equal, show that а с

A:

Q: 7. Which of the following most precisely describes the roots of the equation 3x2 + 4x-1 0?

A: We first compare the given equation with ax2+bx+c=0  so, a=3, b=4, c=-1 The discriminant for the…

Q: If r; and r, are the roots of equation x² – 2x+4 =0, then find Er .

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Q: show that 1+i is a root of the cubic equation 3z^3-5z^2+27z-45=0, find the other two roots

A: 3z3-5z2+27z-45 = 0Using rational root test :±11, ±13, ±31, ±51, ±91, ±93, ±151, ±153, ±451,…

Q: It is given that a and B are the roots of the quadratic equation 2x+4x- 3 = 0. Form a quadratic…

A: If α and β are the roots of the quadratic equation ax2+bx+c=0, then α+β=-baαβ=ca Consider the…

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: 1. Detemine, whether and-5 are roots of the equation 10a –5 = 2a3 - a?.

A:

Q: Determine the roots of y"" - 3y" - y' + 3y = 0

A: The given differential equation is: y'''-3y''-y'+3y=0   So, we can also write as; D3-3D2-D+3y=0

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

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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: Find the roots of the equation z³ – 1 = 0.

A: Given,           z3-1=0

Q: If the roots of the equation a(b – c)x² + b(c – a)x + c (a – b)=0 2 1.1 are equal, show that b а с a

A: Here we will show that 2b=1a+1c

Q: Show that the root of equation x^2×(mx+c)^2=a^2 will be equal of c^2=a^2(1+m^2)

A: Given equation, x2+mx+c2=a2

Q: If 7, and r, are the roots of equationx -2x+4=0, then find r.

A: Given equation, x2-2x+4=0 If r1 and r2 are the roots of the equation, then find ∑ri3.

Q: For what values of the parameter a does the equation x + 2ax³ + x² + 2ax+1=0 have at least two…

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Q: Determine the roots of each equation Y= x^2 + 9x + 3 Y = 3x^2 + 24x - 6

A: The objective of the question is determine the roots of the given equations.

Q: If a + ß and o² = 5a - 3 and ² = 53-3, find the equation whose roots are alß and B/a.

A:

Q: If a and b are roots of x2 - 4x - 21 = 0, where a > b, find the equation whose roots are a/b and…

A: First obtain the roots of the given equation as follows.

Q: x^6+10*x^5+35*x^4+315*x^3+12*x^2-140*x+2.5 then insert a table to draw the graph of the previous…

A: Given equation ; x6+10x5+35x4+315x3+12x2-140x+2.5=0

Q: Let r, r, and r, be the roots of x’ +3x² –5x-4=0, construct the equation whose roots are: 7 (r, +r,…

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Q: If AC = 8x-14 and EC = 2x +11, solve for x. %3D В A

A: Using the property that "The diagonals  of a parallelogram bisect each other"  , we can find the…

Q: Show that the equation  x4 + 4x + c =0 has at most tworeal roots.

A: Given: The method of contradiction is used to prove that the above equation has at most  two roots.

Q: Determine all the roots of R(y)=12y²+11y-5.

A:

Q: Find an equation for each line in the form ax + by = c, where a, b, and c are integers with no…

A: It is given that the given line is passing through the point 0,5 and it is perpendicular to the line…

Q: If the roots of the equation a(b-c)x² + b(c-a)x+ c(a - b) = 0 - are equal, show that 2/b = 1/a +…

A: What is Discriminent: The discriminant of a higher degree equation in one variable determines the…

Q: 1. What are the roots of the equation (x + 1)(4x – 3) = 0? C) x= 1, - D) x= 1 A) x = -1,3 B) x= -1,

A: (x+1)(4x-3)=0⇒(x+1)=0 or (4x-3)=0⇒x=-1 or 4x=3⇒x=-1 or x=34⇒x=-1 ,34

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

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Q: If the roots of the equation x2+2cx+ab=0 are real unequal ,prove that the equation…

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Q: Let r, r, and r, be the roots of x +5x+2=0, construct the equation whose roots are: r, r and r.…

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

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: If a, b, c are in GP and the equation ax² +2bx+c= 0 and dx² +2ex+f=0 have a common root, then is it…

A: Given that a,b,c in G.P and the equation ax2+2bx+c=0 and dx2+2ex+f=0 have a common root.

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: Compute the discriminant. Then determine the number and type of solutions for the given equation.…

A: The standard discriminant form for the quadratic equation ax2 + bx + c = 0 is Discriminant: D = b2 –…

Q: Find the equations with the following pairs of roots. 1. {2, 3} 2. {-3, 1} 3. {4, -2}

A: Use sum of roots and product of roots in the general equation. General equation, x2-(sum of roots)…

Q: If a and B are the roots of the equation x² - 3x + 4 = 0, the equation whose roots are a? + a + 1…

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

Q: 52. The sum of the roots of the equation at + bt + c = 0 is equal to the sum of the squares of their…

A:

Q: If the auxiliary roots of a certain HLDE with constant coefficients are 2, -3, and -3, then the…

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Q: Given that the equation z2 + (p + iq)z + r + is = 0, where p, q, r, s are real and non-zero has a…

A: Introduction :--