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mathematics
precalculus
Precalculus 9th edition Michael Sullivan - Solutions
True or False.Some equations have no solution.
True or False.If the discriminant of a quadratic equation is positive, then the equation has two solutions that are negatives of one another.
True or False.Quadratic equations always have two real solutions.
The quantity b2 – 4ac is called the ______ of a quadratic equation. If it is _______, the equation has no real solution.
To solve the equation x2 + 5x = 0 by completing the square, you would _____ the number ______ to both sides.
Which of the following pairs of equations are equivalent? Explain. (a) x2 = 9, x = 3(b) x = √9, x = 3(c) (x – 1)(x – 2) = (x – 1)2; x – 2 = x – 1
Show that the real solutions of the equation ax2 + bx + c = 0 are the reciprocals of the real solutions of the equation cx2 + bx + a = 0. Assume that b2 – 4ac ≥ 0.
Show that the real solutions of the equation ax2 + bx + c = 0 are the negatives of the real solutions of the equation ax2 - bx + c = 0. Assume that b2 – 4ac ≥ 0.
Find k such that the equation x2 - kx + 4= 0 has a repeated real solution.
Find k such that the equation kx2 + x+ k= 0 has a repeated real solution.
Show that the product of the roots of a quadratic equation is c/a.
Show that the sum of the roots of a quadratic equation is - b/a.
List some formulas that occur in applications. Solve the formula for the indicated variable. Mechanics v = - gt + v0 for t
List some formulas that occur in applications. Solve the formula for the indicated variable. Mathematics S = for r
List some formulas that occur in applications. Solve the formula for the indicated variable. Chemistry PV = nRT for T
List some formulas that occur in applications. Solve the formula for the indicated variable. Mechanics ту? for R
List some formulas that occur in applications. Solve the formula for the indicated variable. Finance A = P(1 + rt) for r
List some formulas that occur in applications. Solve the formula for the indicated variable. Electricity for R R2 R1 ||
Solve the equation. The letters a, b, and c are constants.
Solve the equation. The letters a, b, and c are constants. 2 х — а х — 1 х +а
Solve the equation. The letters a, b, and c are constants. a c, c + 0 х х
Solve the equation. The letters a, b, and c are constants. х х 3 с, а # 0, Ь # 0, а # —b b. la
Solve the equation. The letters a, b, and c are constants. 1 - ax = b, a ≠ 0
Solve the equation. The letters a, b, and c are constants. ax - b = c, a ≠ 0
Use the discriminant to determine whether the quadratic equation has two unequal real solutions, a repeated real solution, or no real solution without solving the equation. 2x2 - 3x - 4 = 0
Use the discriminant to determine whether the quadratic equation has two unequal real solutions, a repeated real solution, or no real solution without solving the equation. 3x2 + 5x - 8 = 0
Use the discriminant to determine whether the quadratic equation has two unequal real solutions, a repeated real solution, or no real solution without solving the equation. 25x2 - 20x + 4 = 0
Use the discriminant to determine whether the quadratic equation has two unequal real solutions, a repeated real solution, or no real solution without solving the equation. 9x2 - 30x + 25 = 0
Use the discriminant to determine whether the quadratic equation has two unequal real solutions, a repeated real solution, or no real solution without solving the equation. x2 + 5x + 7 = 0
Use the discriminant to determine whether the quadratic equation has two unequal real solutions, a repeated real solution, or no real solution without solving the equation. x2 - 5x + 7 = 0
Find the real solutions, if any, of the equation. Use the quadratic formula. x2 + √2x – 2 = 0
Find the real solutions, if any, of the equation. Use the quadratic formula. x2 + √3x – 3 = 0
Find the real solutions, if any, of the equation. Use the quadratic formula. 2x2 = 1 - 2x
Find the real solutions, if any, of the equation. Use the quadratic formula. 4x2 = 1 - 2x
Find the real solutions, if any, of the equation. Use the quadratic formula. 4t2 + t + 1 = 0
Find the real solutions, if any, of the equation. Use the quadratic formula. 4y2 - y + 2 = 0
Find the real solutions, if any, of the equation. Use the quadratic formula. 2x2 + 5x + 3 = 0
Find the real solutions, if any, of the equation. Use the quadratic formula. 2x2 - 5x + 3 = 0
Find the real solutions, if any, of the equation. Use the quadratic formula. x2 + 5x + 3 = 0
Find the real solutions, if any, of the equation. Use the quadratic formula. x2 - 5x - 1 = 0
Find the real solutions, if any, of the equation. Use the quadratic formula. x2 + 4x + 2 = 0
Find the real solutions, if any, of the equation. Use the quadratic formula. x2- 4x + 2 = 0
Solve the equation by completing the square. 2x2- 3x - 1 = 0
Solve the equation by completing the square. 3x2 + x - 1/2 = 0
Solve the equation by completing the square. 1 + 3. 3
Solve the equation by completing the square. 3 x2 16
Solve the equation by completing the square. x2- 6x = 13
Solve the equation by completing the square. x2 + 4x = 21
Solve each equation by the Square Root Method. (3x – 2)2 = 4
Solve each equation by the Square Root Method. (2y + 3)2 = 9
Solve each equation by the Square Root Method. (x + 2)2 = 1
Solve each equation by the Square Root Method. (x – 1)2 = 4
Solve each equation by the Square Root Method. x2 = 36
Solve each equation by the Square Root Method. x2 = 25
Solve the equation. 6x - 5 = 6/x
Solve the equation. 3 = 4 + х — 2 х+ 4
Solve the equation. 4(х — 2) х — 3 3 -3 x(х — 3) х
Solve the equation. x + 12/x = 7
Solve the equation. 25x2 + 16 = 40x
Solve the equation. Solve the equation. 4x2 + 9 = 12x
Solve the equation. x(x + 1) = 12
Solve the equation. x(x - 7) + 12 = 0
Solve the equation. 3x2+ 5x + 2 = 0
Solve the equation. 2x2 - 5x - 3 = 0
Solve the equation. v2 + 7v + 12 = 0
Solve the equation. z2 + 4z - 12 = 0
Solve the equation. x2 = -8x
Solve the equation. x2 = 4x
Solve the equation. |x2 + 3x - 2| = 2
Solve the equation. |x2 + x - 1| = 1
Solve the equation. |x2 + x| = 12
Solve the equation. |x2 - 2x|= 3
Solve the equation. |x2 - 9|= 0
Solve the equation. |x2 - 4| = 0
Solve the equation. |2 - x| = -1
Solve the equation. |x - 2| =
Solve the equation. |3|x = 9
Solve the equation. |-2|x = 4
Solve the equation. |-x| = 1
Solve the equation. |-2x| = 8
Solve the equation. |1 - 2z| = 3
Solve the equation. |1 - 4t| = 5
Solve the equation. |3x - 1| = 2
Solve the equation. |2x + 3| = 5
Solve the equation. |3x| = 12
Solve the equation. |2x| = 6
Solve the equation. (2х + 3)(х — 1) х — 1 2х + 3
Solve the equation. 3 10 (x + 5)(x – 2) x + 5 || 2.
Solve the equation. (x - 5)(2x) = (x - 5)(4)
Solve the equation. (x + 2)(3x) = (x + 2)(6)
Solve the equation. -2 -3 x + 1 x + 4
Solve the equation. 3 2 2x 3 х+5
Solve the equation. 4z3 – 8z2 = 0
Solve the equation. t3 – 9t2 = 0
Solve the equation. x3 = x2
Solve the equation. x2 = 9x
Solve the equation. w(4 – w2) = 8 – w3
Solve the equation. z(z2 + 1) = 3 + z2
Solve the equation. (x + 2) (x – 2) = (x – 3)2
Solve the equation. (x + 7)(x – 1) = (x + 1)2
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