(a) For any real number c , the quadratic equation x2 + x – c² = 0 has two distinct (real) solutions. (b) If a > 4 , then the equation ax? + 4x + 1 = 0 has no (real) solutions. (c) If b2 – 4ac > 0, then the quadratic equation ax? + bx +c=0 has at most one solution. -

Q: Solve the equations for x . ax +2x =a x = if a ≠ −2.

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Q: What is the solution to this quadratic: x2-6x +9 0 {3) {-3+3i/2, -3 – 3i/2} {-6+6i/2, -6 – 6i/2} {0,…

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Q: For what value of a will the equation ax² + 4x = 1 have exactly one solution?

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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: Show that the equation x^3 + 6x^2 − 4 = 0 has exactly one solution p^∗ in the interval [0, 1].

A: We used Rolles theorem.

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: 5- Solve the following linear algebraic equations using the Gauss elimination method: 3x, - 2x2 +…

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Q: 1- Solve the set of simultaneous equations below: a- 2x-4y=-24 9x-3y=-3 b- 2x+3y=27 6x+9y=81

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Q: 2 3 Find all real solutions to the equation V2x- 1 1+ 2x+1

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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: 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: 2x2+2x+1 Q2/ Solve for x, <1 x2-3x-1

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Q: 4) Find the number of real and nonreal solutions for x3- x2 +3x -3 = 0

A: We have to find out

Q: The monthly revenue in dollars from the sale of "x" units of a certain colon cancer drug is given…

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Q: ] Prove that the equation 2" – x = 1+ 4/x has a solution greater than 0.

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Q: Solve for the general solution of (D: - 5D + 6)y = 4e* using method of undetermined coefficients.

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Q: question 10

A: Find all real solution to the equation

Q: What are the solutions to x² - 8x = 0? O x = 0 and x = -8 O x = 0 and a = 8 O x = 0 and x = = v8 O x…

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Q: = (; ). -3 Find the general solutions of X' = AX with A = 1 -2

A: Consider the provided question,

Q: Find k such that the equation kx2 + x + k = 0 has a repeatedreal solution

A: Consider the provided equation, kx2+x+k=0 Find the value of k of the provided equation has a reacted…

Q: If x2 + y2 = 16 and x-y 3, then what is x? If there are two possible answers, then enter the larger…

A: Given that      x2 + y2 = 16     and     x - y = 3 Here we have to find the value of x .

Q: 23/1-If-2<x<4 then determine a and b in(a<-2x+1<b). 2-Solve +3xr²+3x+10 x-1

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Q: 3 Find the general solution of i = Ax, where A = -8-

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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: 2 3 Find all real solutions to the equation V2x – 1 = 1+ V2x + 1

A: The equation given in the question is: Find the least common multiplier of  Multiply both sides of…

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

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Q: Find the general solution of 17y" + 5y' - 25 = 0

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Q: y" - y = x²ex + 5

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Q: 3(x-2)+7x=1/2(6x-2) has how many solutions?

A: 3(x-2)+7x=1/2(6x-2) has how many solutions?

Q: If a, b, c are integer powers of 2, prove that equation a³ + 64 = c does not have solution,…

A: Given,a,b,c are integers of the form 2k, k∈Na3+b4=c5

Q: Find the general solution of z'-2/x (z) =2/3x^4

A: l

Q: Find all real solutions. (a) x - x - 12 = 0 (b) 2x2 + 4x +1 = 0 (c) 3 – Vx – 3 = x (f) 3|x - 4 = 10…

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

Q: Find the general solution to 22" +3ry = 2x3, r> 0. x>0.

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Q: Solve Ax = b, where -4 X1 3 ... -4 6 -4 X2 ... 1 -4 6 -4 1 X3 ... A = 1 -4 6 -4 0 0 1 -4 X9 7 X10 1.

A: We need to solve Ax=b, where A=6-410000000 -46-41000000 1-46-4100000 01-46-410000 001-46-41000…

Q: quadratic equation

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Q: (4) Find B such that the equation ßx² + x + ß : 0 has a repeated real solution.

A: Question no..4 Note : the equation has a repeated real solution, if the discriminant is 0.

Q: Solve using any method. -x- 2y = - 13 - 4x+ 2y=2 A inconsistent

A: Given equation  -x-2y=-13      (1) -4x+2y=2          (2)

Q: 2. The sum of the roots of the quadratic equation x²-x-6=0 is given by 2 O

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Q: If x = 9 is solution of An (x²+15a²) – An (a – 2) =àn 8ax then а-2

A: Introduction :

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: 1. Find how many real solutions x2 + 6x + 24 has. What are those solutions (real or otherwise)?

A: Since you have posted multiple questions as per our guidelines we are allowed to answer the first…

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

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

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: 6. Given the equation x1 + x2 + X3 + x4 = 40, where x1, x2, X3, and x4 are integers. How many…

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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: (4) Find β such that the equation βx2+ x + β = 0 has a repeated real solution.

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Q: given (x^2 - 4x -3x)^(x^3-16x) = (x^2- 2x+2)^(x^3-16x) has the solution of a, b and а, С. If…

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