Solve the following 3 quadratic equations using the quadratic formula: -b±yb²-4ac 2а a) 4x² + 12x + 9 = 0 6) x² – x + 3 = 0 %3D c) 2x2 + 5x – 2 = 0 d) The value under the radical (62 – 4ac) is called the discriminant. | Using the examples that you calculated above, explain how the discriminant determines how many real solutions there are for a quadratic equation.

Q: Use Descartes's rule of signs to find the number of positive and the number of negative solutions of…

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A: given quadratic equation is (3x+6)(4x-20)=0  now, if ab =0 for any numbers a,b then either a=0 or…

Q: If the roots of the equation a(b - c)x² +b(c - a)x + c (a - b) = 2 11 are equal, show that ==±+:

A: We can use properties of square of three no. To solve the problem

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

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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: What are the roots of the equation x2 + 2x + 37 = 0 in simplest a + bi form?

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Q: If a and 3 are the roots of the quadratic 3r² – 4.x + 6 = 0, find the value of ( + )

A: We have to solve given problem:

Q: Show that the product of the roots of a quadratic equation is c/a .

A: Consider the quadratic equation ax2+bx+c=0 Also consider that α and β are the roots of the quadratic…

Q: 1. Consider the quadratic equation 3x -6 = 2x. (a) What is the value of the discriminant? (b) What…

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Q: Find all 4 roots of the equation z4+1=0.

A: Concept:

Q: 15 (-4i + 2) =

A: We have to solve : 15.(- 4i +2) = ?

Q: (b) The roots of the quadratic equation 3x-11x+9=0 are a and B. Form a quadratic equation whose…

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Q: A dolphin dives down into the ocean and resurfaces along a path that is modeled by x² - 8x + 4y = 0,…

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

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Q: In the following complex equation (28 - j3) * (A + j4) = (3 + j71) * (B + j3) Find the value of the…

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Q: Which of these equations has two real roots: Select one: O a x2 - 4x + 4 =0 O b. x2 - 10x + 100 = 0…

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Q: Find one of the four solutions of (6x – 9x +4) -5(6z - 9x + 4) +5 = 0. Write your solution using…

A: To solve: 6x2-9x+42-56x2-9x+4+5=0 Substitute 6x2-9x+4 = y

Q: Find the change of variable x = Py that transforms the quadratic form x' Ax into y' Dy as shown. 2 −…

A: Matrix A is of quadratic form ( from LHS) and D be diagonal matrix of eigen values (from RHS)…

Q: 25x2+16y2-600x-256y+4224=0 What is the standard form of the equation?

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Q: What are the roots of the equation x2 + 14x + 50 = 0 in simplest a + bi form?

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Q: Determine the solutions of each quadratic equation by extracting the square roots a) (Зх — 3)2 — 363…

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Q: Solve the roots of the following quadratic equations. 3(x+2)^2 = 48

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Q: By using the method of completing the square, show that the equation 4x2 +3x+5=0 has no real roots.

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Q: If a and b are the roots of the quadratic equation (x - 2023)(x-2024) = 2025, then (2025-a) (2025-b)…

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