1. Equations & Inequalities

The Quadratic Formula

Textbook Question
Find all values of x satisfying the given conditions. y₁ = x - 1, y₂ = x + 4 and y₁y₂ = 14
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Multiple Choice
For a quadratic equation in standard form $a x^{2} + b x + c = 0$ , what expression gives the discriminant?
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Multiple Choice
Which mathematician is most commonly credited with introducing a general method equivalent to the modern quadratic formula for solving equations of the form $a x^{2} + b x + c = 0$ ?
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Multiple Choice
Which equation shows the quadratic formula used correctly to solve $a x^{2} + b x + c = 0$ for $x$ ?
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Multiple Choice
Which mathematician is most commonly credited with developing the general solution for quadratic equations (often called the quadratic formula) in the 9th century?
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Textbook Question
Solve each polynomial equation in Exercises 1–10 by factoring and then using the zero-product principle. $3 x^{4} = 81 x$
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Multiple Choice
Solve the given quadratic equation using the quadratic formula. $3x^2+4x+1=0$
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Multiple Choice
Solve the given quadratic equation using the quadratic formula. $2x^2-3x=-3$
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Multiple Choice
Determine the number and type of solutions of the given quadratic equation. Do not solve.
$x^2+8x+16=0$
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Multiple Choice
Determine the number and type of solutions of the given quadratic equation. Do not solve.
$-4x^2+4x+5=0$
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Textbook Question
Solve each equation in Exercises 1 - 14 by factoring. $2 x (x - 3) = 5 x^{2} - 7 x$
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Textbook Question
Solve each equation in Exercises 1 - 14 by factoring. 7 - 7x = (3x + 2)(x - 1)
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Textbook Question
Solve each equation in Exercises 1 - 14 by factoring. 10x - 1 = (2x + 1)²
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Textbook Question
Solve each equation in Exercises 15–34 by the square root property. (x + 2)² = 25
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Textbook Question
Solve each equation in Exercises 15–34 by the square root property. $3 (x - 4)^{2} = 15$
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