In the given questions ,characterize the solutions to the following equations by evaluating the discriminant D2   x3 - 3x + 52 = 0

Q: Find the real solutions of the following equation. 2x+7-x+15 = 1

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Q: (Dª +2D³ + D² +12D+20)y = 0

A: We have to find the general solution of the equation.

Q: What is the discriminant of the quadratic equation ax + bx + c = 0? Find the discriminant of 2r - 3x…

A: The discriminant of the quadratic equation ax2+bx+c=0 is given by D=b2-4ac. The rules that defines…

Q: Find all solutions of the equation x2y' = y3 − 5x2y3 explicitly

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Q: Which of the following is the standard equation of 9y² – x² + 2x+ 54y+62

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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: The roots of the equation x2+(m-2)x+4m-6=0 are x1 and x2. So: what is x,2 + x2² = ? at least?

A: Solution: The objective is to find x12+x22

Q: Which of the following are the approximate solutions of the quadratic equation 3x + 20x + 32 = 0?

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Q: iven as y" + 2y'-3y = 2x³ + x - 3. Solve the particula PI).

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Q: Solve the equations below for x, if pos 3x-1 a. %3D 4. 11 b. 6 – 5(2x – 3) = 4x + 7 %3D 3x c. + 2 =…

A: The general rules for solving equations for x are: i) simplification of each sides of the equation…

Q: fa is a root of the equation 4x² + 2x - 1 = 0, then prove that ²3 is the other root

A:

Q: Find the value of p for which the roots of the equation px(x-2)+6=0 are equal

A: Given the equation px(x-2)+6=0. We need to find the value of p for which the roots of the equation…

Q: The discriminant of the quadratic equation 4x+7z-4 0 is O 15

A:

Q: 4. For what value of b will the quadratic equation 16x? + bx + 9 = 0 have one root?

A: Given a quadratic equation 16x2+bx+9=0 and we have to find the value of b so that the equation have…

Q: In the given questions ,characterize the solutions to the following equations by evaluating the…

A: x3-3x+52=0

Q: Find all real solutions of the equation.

A: Given, 4x2-4x3=x

Q: tind the general Solution of the different ial equation! PxLx-2)-Pl2yー2xyーX42)+y+リ=0 +ソ=。

A: Find the general solution of the ODE:xx-2p2-2y-2xy-x+2p+y2+y=0

Q: Compute the value of the discriminant and give the number of real solutions of the quadratic…

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Q: For what value of k does the equation kx2 -4x + k = 0 has two equal real roots?

A: Given, kx²-4x+k=0 a=k b=-4 c=k

Q: Solve the equation 12r + 16x - 5x – 3 = 0 given that - is a root. %3D

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Q: What is the discriminant of the equation ar+ bx +c= 0? D=

A: Given equation :

Q: Compute the value of the discriminant and give the number of real solutions of the quadratic…

A: Suppose ax2+bx+c = 0 is a quadratic equation. The discriminant of the quadratic equation is b2-4ac.…

Q: For Exercise, use A = and B = 4 and solve for x. 61 -2. 4 ЗВ - А %3D -2X

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Q: Find the general solution of the following equation * + 5 + 6y = 2x

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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: 43. Given that r is a root of the quadratic equation x² - 3x - 5 = 0, find the value of 2r² – 6r +…

A: Given: r is a root of quadratic equation x2-3x-5=0. To determine: Value of 2r2-6r+1

Q: For what values of p does the equation, 5p+x2 =−10x−5, have a single solution?

A: for single solution quadratic equation should be a whole square.

Q: Which shows all of the solutions of the equation x 16 %3D 121 4 11 O z = +

A: To find- Solutions of the given equation.

Q: Compute the value of the discriminant and give the number of real solutions of the quadratic…

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Q: Solve the given diffential equation by undtermeined coefficients: y'' + y' - 6y = 12x

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Q: Compute the discriminant. Then determine the number and type of solutions for the equation. 7x² -x +…

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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: Find by the LU factorization method solution of the following equation (2x + 3y = -1 (x=y=1

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Q: Find the value of x that intersect to the given equation.. 2x1 + 5x2 = 16 3x1 + x2 = 11

A: Given that  2x1+5x2=163x1+x2=11 We have to find the value of x=x1,x2 that intersects the given…

Q: In the given questions ,characterize the solutions to the following equations by evaluating the…

A: x3-32x+24=0

Q: Use the method of undetermined coefficients to determine the form of a particular solution to the…

A:

Q: Use the techniques presented in this section to find all solutions of the given equation   8x3 +…

A: Given: 8x3+12x2+150x+25=0 To Find: All solutions of the given equation. Concept: if…

Q: The general solution for Legendre equation (4 – x2)y" – 2xy' + n(n + 1)y = 0 is %3| -

A: Given The given equation is 4-x^2y"-2y'+nn+1y=0

Q: In the given questions ,characterize the solutions to the following equations by evaluating the…

A: Given: f(x)=x3-55x-72⇒x3-55x-72=0

Q: In the given questions ,characterize the solutions to the following equations by evaluating the…

A: x3-32x+24=0⇒x3+0x2-32x+24=0 Now comparing with ax3+bx2+cx+d=0, we get a=1,  b=0,  c=-32  &…

Q: 31. Find the discriminant of the equation and give the number and type of solutions of the equation.…

A: We can find the answer as below

Q: Solve the following equation with special factors. 27x-3x2 0 %3D The values of x are and

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Q: the sum of the roots of the equation 1/(x + a) + 1/(x == 1/c is zero, then prove that the product of…

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Q: Find all solutions for x in the following equations. A. 16cos^2x=4 B. Ckt^2x-3cotx+2=0

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Q: For what values of b the equation       x2 - 4x + 4b = 0 has two real solutions?

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Q: Given the equation below. Give what is being asked. sec23xdx a In(1+4tan3x) + C 1+ 4tan3x Find: a +…

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Q: Given the equation: y = (eln x², find y. A In x B 2(In x) / x (c) 2x D 2 elnx

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Q: For what values of k will the quadratic equation x2 + kx+ 16 = 0 have two equal real roots?

A: The values of k are, - 8 & 8.

Q: С. The possible x and y intercepts of x+3 y=- x² +6x+9 O -3, попе,

A: Given y=x+3x2+6x+9

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.