Nonlinear Equations
Practice solving nonlinear equations beyond the quadratic case.
12 questions
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In the xy-plane, a line with equation 2y = 4.5 intersects a parabola at exactly one point. If the parabola has equation y = −4x 2 + bx, where b is a positive constant, what is the value of b?
Hard - View question →
x + 7 = 10 (x + 7) 2 = y Which ordered pair (x, y) is a solution to the given system of equations?
Medium - View question →
y = 4x y = x 2 − 12 A solution to the given system of equations is (x, y), where x > 0. What is the value of x ?
Medium - View question →
The function g is defined by g(x) = (x + 14)(t − x), where t is a constant. In the xy-plane, the graph of y = g(x) passes through the point (24, 0). What is the value of g(0) ?
Medium - View question →
The function g is defined by g(x) = x(x − 2)(x + 6) 2 . The value of g(7 − w) is 0, where w is a constant. What is the sum of all possible values of w ?
Hard - View question →
(d − 30)(d + 30) − 7 = −7 What is a solution to the given equation?
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If 4√ 2x = 16, what is the value of 6x ?
Medium - View question →
Which quadratic equation has no real solutions?
Medium - View question →
What is a root of x(x – 1)(x + 1) = 27 – x?
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The cube of a number minus twice its square is equal to 80 times the number. If the number is greater than 0, what is the number?
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Four times the cube of a number is equal to 48 times the number minus four times the square of the number. If the number is greater than 0, what is the number?
Hard - View question →
The product of 3 consecutive positive integers is equal to 56 more than the cube of the first integer. What is largest of these integers?
Hard