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Solving Quadratic Equations

This worksheet covers Solving Quadratic Equations, which is part of the Introduction and Prerequisite module in the SAT Math Destroyer Crash Course course. Practice problems are designed to strengthen key concepts and build confidence.

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Solving Quadratic Equations

Introduction and Prerequisite • SAT Math Destroyer Crash Course

Set 3 — Mastery

If $x^{2} - 5x + 6 = 0$ , what are the roots of the equation?

$x = 2$ and $x = 3$

$x = -2$ and $x = -3$

$x = 1$ and $x = 6$

$x = 0$ and $x = 5$

A projectile is launched from the ground with an initial velocity of $v_{0}$ . Its height $h$ as a function of time $t$ is given by $h(t) = -16t^{2} + v_{0}t$ . If $v_{0} = 32$ , what is the maximum height reached?

$64$

$128$

$256$

$16$

If $x^{2} + 4x + 4 = k$ , what value of $k$ makes the equation have exactly one solution?

$8$

$4$

$0$

$16$

Solve for $x$ : $2x^{2} - 8 = 0$ .

$x = 2$ and $x = -2$

$x = 4$ and $x = -4$

$x = 0$ and $x = 4$

$x = 4$ and $x = -4$

A gardener is creating a rectangular garden with an area of $A = 100$ square feet. If the length is $x$ feet, what is the quadratic equation in terms of $x$ if the width is expressed as $w = \frac{100}{x}$ ?

$x^{2} - 100 = 0$

$x^{2} + 100x - 10000 = 0$

$x^{2} - 100x + 100 = 0$

$x^{2} + 100 = 0$

If the roots of the quadratic equation $x^{2} + bx + c = 0$ are $-2$ and $-3$ , what is the value of $b + c$ ?

$5$

$6$

$7$

$8$

A company's profit can be modeled by the quadratic equation $P(x) = -3x^{2} + 12x$ , where $x$ is the number of units sold. What is the maximum profit?

$12$

$18$

$24$

$36$

What are the roots of the equation $3x^{2} - 12x + 9 = 0$ ?

$x = 1$ and $x = 3$

$x = 2$ and $x = 3$

$x = 3$ and $x = -1$

$x = 2$ only

If $x^{2} - 4x + 4 = 0$ , what is the vertex of the parabola represented by this equation?

$(2, 0)$

$(2, 4)$

$(0, 4)$

$(0, 0)$

10.

What is the value of $k$ such that the equation $x^{2} + kx + 9 = 0$ has no real solutions?

$k = 6$

$k = 0$

$k = -6$

$k = 9$

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