If r is the only (repeated) real root to the auxiliary equation ar2 + br + c = 0, then general solution ?

Q: Find the general solution of the Following problem? 6y" - 5y' - 6y = 0

A: Given Data The differential equation is 6y’’-5y’-6y=0.   Let,

Q: If the general solution of (2x2 – 3y2)y' = 2xy is y“ Iny*| + xª Cy“, what is the value of b? A 1 2…

A: The given equation is; (2x2-3y2)y'=2xy.

Q: For what value of c does the equation x^2 - 10x + c = 0 have one solution

A: Given equation is x2-10x+c=0 find the value of c , which has one solution

Q: 10— 5л — 3 + ут+7

A: As per our guideline if multiple questions are posted we are supposed to answer only the first one.…

Q: If the roots of the equation ax²+bx +c = 0 be a and s and those of the equation b - 4ac Ax + Bx +C =…

A: Introduction :

Q: x = -1 is a solution to 8x + 4 > 6x-2. O True O False

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Q: a) For what real values y, does the equation 2x2 - 4y - 135 = x - 2y2 have real solutions? Use exact…

A: a) Find out for what real values y, the equation 2x2-4y-135=x-2y2 have real solution. First rewrite…

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

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Q: Solve the IVP, explicitly if possible. 3y x+9(-7)=1 (x– 7)* 8. y=(x+9)3 (x + 9|) yl = (x+9|)

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Q: How many non-negative integer solutions are there to the equation xi + x2 + x3 = 13, if we insist…

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Q: Find the values that make the equations x1 + x2 + 3x3 = 3 x1 + 2x2 + 4x3 = 3 x1 + 3x2 + ax3 = b…

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Q: If a, b, c are integer powers of 2, prove that equation a³ + b* = c° does not have solution,…

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Q: 12. Show that the equations p² +q? =1 and (p² +q³)x= pz are compatible and hence find its solution.

A: The equation are, p2+q2=1    ⋯1 And p2+q2x=pz                    ⋯2 To show that these equations are…

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

A: Given a,b,c are in g.p So the ratio will be same ba=cbb2=acb=ac ---- {1}

Q: Find the general solution of the Following problem? 4y" + 16y' + 52y = 0

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Q: The linear Diophantine equation 256x + 478y = 9 has no solution. True False

A: True or False

Q: what is the general solution of y (1 + 3 ) y - ju? =D4+3x + Ce =D4+3x Ce* %3D 4 3x + Ce %3D y = 4…

A: We will find out the required solution.

Q: Find the general solution of the Following problem? y" - 2y' - 3y = 0

A: y''-2y'-3y=0 Auxiliary equation       m2-2m-3=0 =>m2-3m+m-3=0 =>m(m-3)+1(m-3)=0…

Q: Prove that the equation x2(a2+b2)+2x(ac+bd)+(c2+d2)=0 has no real root ,if ad is not equals to bc

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Q: The equation –12x + 5 = 8x has x = - as the solution. %3D 4 O True O False

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Q: 3) Given that p= (1    -1                                 3    2) Use p-1 to solve the…

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Q: Find the general solution og the differencial equation: CD-4D+3)y x + eex t x2

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Q: How many non-negative integer solutions are there to the equation x1 + x2 + x3 = 13, if we insist…

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Q: Find the general solution of the Following problem? 16y" - 24y' + 9y = 0

A: Given:16y"-24y'+9y=0

Q: If [x² - 2x + a] = 0 has no solution, then find the values of a

A: We have x2-2x+a=0⇒x2-2x+a∈[0, 1) Given that equation has no solution ⇒x2-2x+a∉[0, 1)

Q: The solution of v(x+6)+6=9 is: O x = 11 X = -1 O x = 3 no real solution

A: We need to solve the equation x+6+6=9

Q: Find the general solution of the Following problem? 9y" + 12y' + 4y = 0

A: Given: 9y"+12y'+4y=0 we know that solution of given differential equation is given by y=aec1x+bxec2x…

Q: For what value of a, the equation(a? -a-2)x² +(a² - 4) x+a² - 3a +2=0 will have more than two…

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Q: Solve for y, where y is a real number. /2y+12+1= 3 If there is more than one solution, separate them…

A: Square both sides

Q: Find all real solutions of teh following equation, rounded to the nearest tenth: 3x4 + 4x3 - 7x2 -…

A: Solutions are the values of x for which the expression dissolves to zero. Zeroes of a polynomial are…

Q: 10. Find all real solutions to the equation V2x - 1 = 1+ ν2α+1.

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Q: What is the solution to this equation? 6x+ 10 - 2x= 7+ 23 O A. x= 15 О В. х%3D 2 O C. x = 5 O D. x=…

A: To find the solution of the equation 6x+10-2x=7+23

Q: Question 3. Apply the Method of Undetermined Coefficients to solve x" − 2x² + x = 2et

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Q: What is the positive solution to the 1,2 equation 0 = x – 4? O1 O4 O -4 O-1

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Q: Hence or otherwise solve the equation x²y" – 4ry + 6y = In r². %3D

A: The given problem is to find the solution for the given non homogeneous differential equation. Given…

Q: given that y = 2x^3 - 9x^2 + 12x + 2 = k has three solutions , kind the possible values of k

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Q: What is the average of the two solutions of the arbitrary quadratic equation ax^2 +bx + c = 0?…

A: The given arbitrary  equation is : ax2+bx+c = 0we know that sum of roots = -baAverage of roots =…

Q: 1. Consider the equations 3(x – 2)(x + 3) = 0 and (2x-4)(3x + 9) = 0. %3D Do they have the same…

A: To solve the above problems

Q: If g(x)=2cos(7x + π), for which values of k does the equation g(x) = k, have no solutions?

A: Given: Find the range of the function g(x)

Q: Find the general solution of the Following problem? 6y" - 5y' - 4y = 0

A: Solution:-  The given differential equation is  6y''-5y'-4y=0................(1)

Q: x= -1 is a solution to 8x + 4 > 6x-2. O True O False

A: Given that:  x=-1 is a solution to 8x+4>6x-2

Q: How many real-number solutions are there to the quadratic equation 2x2 + 5x + 1 = 02 a. eslim b. 1…

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Q: Find the general solution of the Following problem? 4y" + 4y' + 5y = 0

A: Consider the following differential equation: 4y''+4y'+5y=0 Characteristic equation of the above…

Q: Solve the following by Repeated root Method Question 4 X³+ 5x² + 7x-3 = 0

A:

Q: Find the general solution of the Following problem? 6y" + 13y' - 5y = 0

A: Given DE is,               6y"+13y'-5y=0   So its  auxiliary equation is given by,…

Q: 3. For a certain quadratic equation ax? + bx +c = 0, the 2 solutions are x = - and x =2. Which of…

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

A: The quadratic equation is given as ax2+bx+c=0 Its roots are given by x = -b±b2-4ac2a Hence its roots…

Q: ax + bx +c bx-c x+3 x+9 After solving for x, you get x=1;x=0;x=-9;x-3 Which of these are extraneous…

A: The equation                    4=ax2+bx+cx+3+bx-cx+9 After solving for x, we get x = 1, x = 0, x =…

Q: Show that the real solutions of the equation ax2 + bx + c = 0 are the negatives of the real…

A: Show that the real solutions of the equation ax2 + bx + c = 0 are the negatives of the real…

Q: Solve for x: - 3x 1 1 5x 15 - 6 – 6x + 6 (no fractions) (in the form ax? + bx + c = 0 ) x = (type:…

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Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.