a) Factor f(x) = 2x3 + 7x2 − 14x − 40, given that −4 is a zero of f. b) Solve the equation. 2x3 + 7x2 − 14x − 40 = 0

Q: Find all real solutions of the equation. x4 + 4x3 + 2x2 = 0

A: The equation is a statement that consists of equal symbol between two algebraic expressions. The…

Q: Solve using the zero-factor property: (a) r² – 5x + 6 = 0 (b) –4z² + z = -3

A: Part a,Given,           x2-5x+6=0

Q: Assume the quadratic equation x squared +kx- 8 factors.  Give three possible values for k, one of…

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Q: a. Factor f(x) = 9x - 33x + 19x - 3, given that 3 is a zero. b. Solve. 9x - 33x + 19x – 3 = 0

A: Given function: fx=9x3-33x2+19x-3 3 is a zero of fx, that is x-3 is a factor of fx.

Q: Find all real solutions of the equation 7n2=28.

A: Consider the given equation.

Q: " one root of the quadratic equation kx² - 6x + (2k – 3) = 0 is the reciprocal of the other root,…

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Q: What value for a will result in an equation with infintely many solutions? a(x + 5) = 3x + 15

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Q: 13. Solve for A and B. - 7x +8 A B %3D 3x +x-2 3x-2 x+1

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Q: Find all real solutions of the equation.

A: 2x2+3x-12 = 0                  by using quadratic formula.…

Q: Solve the qudaratic equation  by factorization x2+x-(a+1)(a+2)=0

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Q: Find all real solutions of the equation. 8 - 2x = 14 + x

A: To find all the real solutions of the given equation: 8-2x=14+x

Q: Find all real solutions of the equation.

A: x2x+7-x+1x+3=1 Simplify left side of given equation  Make common denominator of left side…

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: find the all solutions of eguation 2-lo2+25 =-1+3i

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Q: any solutions does the equation 2 + 6 (x 4) = 3x - 18 + 3x have?

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Q: Find all real solutions of the equation.

A: The given equation is, 2xx2+1=1 On simplifying the equation, we get 2xx2+1=1x2+1=2xx2-2x+1=0

Q: Find all real solutions of the equation. x2/3 - 4 = 0

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Q: Find all real solutions of the equation. x2 - 6x + 1 = 0

A: Given: x2-6x+1=0 Determine the roots of the equation using: x=-b±b2-4ac2a

Q: Find all real solutions of the equation.

A: Given, 4x2-4x3=x

Q: Find all real solutions of the equation. x3/2 - 10x1/2 + 25x-1/2 = 0

A: Consider the equation, x32-10x12+25x-12=0

Q: Compute the discriminant of 3x2 - 2x + 5 = 0. What does the discriminant indicate about the number…

A: Given: 3x2-2x+5=0 we know that every quadratic equation has two solutions, if DiscriminantD of…

Q: Find all real solutions of the equation. 7x3 - x + 1 = x3 + 3x2 + x

A: To find: The real solution of the equation: Given: The equation is 7x3-x+1=x3+3x2+x. Concept used:…

Q: Find all real solutions of the equation. x4 - 8x2 - 9 = 0

A: We have to find all real solutions of the equation: x4-8x2-9=0 Solving the equation by middle term…

Q: Find all real solutions of the equation. x5 - 3x2 = 0

A: First, take out the common term from the equation x5-3x2=0. x5-3x2=0x2x3-3=0 Since we know that if…

Q: The solution set for x−7− square root of 36x =0 consists of

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Q: Find all real solutions of the equation. x4 - 4x2 + 3 = 0

A: We have to find all real solutions of the equation: x4-4x2+3=0 Solving the equation by middle term…

Q: Find all real solutions of the equation. x-1/2 - 2x1/2 + x3/2 = 0

A: The rational exponents is a exponents which are having as a fractional numbers. The…

Q: solve using the zero factor property 45-t2=0

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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: x² – 8x – 2 = 0 - %3D -

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Q: Find all real solutions of the equation.

A: Given that the equation, 11 - x2 - 211 - x2 = 1 To solve the equation and find out all real…

Q: Find all real solutions of the equation. (3x + 5)4 - (3x + 5)3 = 0

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Q: quadratic

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Q: Find all real solutions of the equation. x2 - 9x + 14 = 0

A: Given equation: x2-9x+14=0

Q: Solve for x by factoring. Must show all work  a) 3x2-12x=0 b) x2+4=-4x c) 3x2-x-10=0

A: (a) We have, ⇒3x2-12x=0⇒3x(x-4)=0         (taking 3x common)∴ 3x=0     and    x-4=0⇒x=0      and…

Q: A root of equation ax2 + bx + c = 0 (where a, b and c are rational numbers) is 5 + 3v3. What is the…

A: The given root of ax2+bx+c=0 is 5+33Tio find the value of a2+b2+c2a+b+c

Q: the quadratic equation x2 + x = 3kx- k2 has two different real roots. find the range of value of k

A: The given problem is to find the range of value of k for which the quadratic equation has two…

Q: 8.) Solve the given quadratic equation using the factoring method. x² +5x+2 = -2x² +7x+7

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Q: Find the real solutions of equation x4+4x3+2x2-x+6=0

A: To determine the real solutions of given equation.

Q: 4. For what value of b will the quadratic equation 16x² + bx + 9 = 0 have one root?

A: Given,            16x2+bx+9=0To find : The value of b.

Q: Find the real solutions of the equation: (√2x + 3) - (√x + 2) = 2

A: Given equation is 2x+3-x+2=2. To find the real solutions of the equation. Solution: Given equation…

Q: Find all real solutions of the equation.

A: Given 1+x+1-x=2 To find all the real solutions, 1+x+1-x=2 Squaring on both sides, 1+x+1-x2=22…

Q: b) Solve algebraically for x: 54x = 125*-1

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Q: Find all real solutions of the equation.

A: Given equation,  x-9-3x=0.   It is simplified as follows: x-9-3x=0 Squaring both sides,…

Q: Find all real solutions of the equation. x3 - 5x2 + 6x = 0

A: Given equation is x3-5x2+6x=0.

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: Solve the equation x^6 - 4x^4 =0 If you have more than one solution, separate them with commas, as…

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Q: Find all real solutions of the equation (x – 3) = 9. and x2 = with x1 < 2

A: The solution is given below

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

A:

Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.