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判别式・相切与根的个数挑战

\( y+k=x+26 \) 
\( y-k=x^2-5x \) 
In the given system of equations, k is a constant. The system has exactly one distinct real solution. What is the value of k?
知序中文精讲
Bluebook试题7 · 原库模块 3 · Q16作答 ↗
判别式・相切与根的个数挑战

\( 4x^2-px+w=-86 \) 
In the given equation, p and w are integer constants. The equation has exactly one real solution. Which is NOT a possible value of w?
知序中文精讲
2026年3月国际A卷 · 原库模块 3 · Q20作答 ↗
判别式・相切与根的个数挑战

\( y=-3x^2-34 \) 
\( y=qx-31 \) 
In the given system of equations, \( q \)is a positive constant. The graphs of the equations in the given system intersect at exactly one point, (\( x,\ y \)), in the \( xy \)-plane. What is the value of \( x \)?
知序中文精讲
2023年5月练习卷(易) · 原库模块 1 · Q7作答 ↗
判别式・相切与根的个数挑战

\( y=3x^2+32 \) 
\( y=px+29 \) 

In the given system of equations, p is a positive constant. The graphs of the equations in the given system intersect at exactly one point \( (x,\ y) \) in the xy-plane. What is the value of x?
知序中文精讲
2026年5月国际A卷 · 原库模块 2 · Q9作答 ↗
判别式・相切与根的个数挑战

\( -x^2+bx-49=0 \) 
In the given equation, b is an integer. The equation has no real solutions. What is the least possible value of b?
知序中文精讲
2025年8月国际A卷 · 原库模块 2 · Q22作答 ↗
判别式・相切与根的个数进阶

\( y=2x^2-15x+23 \) 
\( y=x+a \) 
In the given system of equations, a is a constant. The graphs of the equations in the given system intersect at exactly one point, (x, y), in the xy-plane. What is the value of x?
知序中文精讲
2024年8月A卷 · 原库模块 1 · Q16作答 ↗
判别式・相切与根的个数进阶

y = 2x2 - 21x +64
y = 3x + a
In the given system of equations, a is a constant. The graphs of the equations in the given system intersect at exactly one point, (x, y ), in the xy-plane. What is the value of x?
知序中文精讲
Bluebook试题2 · 原库模块 1 · Q22作答 ↗
判别式・相切与根的个数基础

\( -3x^2+bx-12=0 \) 
In the given equation, b is a positive integer. The equation has no real solution. What is the largest possible value of b?
原库参考解析
2023年10月B卷练习(数易) · 原库模块 2 · Q18作答 ↗
判别式・相切与根的个数挑战

\( 18x^2-24x+c=0 \) 
In the given equation, \( c \) is a constant. The equation has exactly one solution. What is the value of \( c \)?

原库参考解析
2023年11月A卷 · 原库模块 2 · Q11作答 ↗
判别式・相切与根的个数挑战

\( y=x-c \) 
\( y=-4\left(x-6\right)^2 \) 
In the given system of equations, c is a constant. The system has two distinct real solutions. Which of the following could be the value of c?

原库参考解析
2023年11月A卷 · 原库模块 2 · Q19作答 ↗
判别式・相切与根的个数挑战

Which quadratic equation has exactly one distinct real solution?
原库参考解析
2023年12月A卷 · 原库模块 2 · Q9作答 ↗
判别式・相切与根的个数挑战

\( x^2+38x+c=0 \) 
In the given equation, c is a constant, The equation has no real solutions if c > n. What is the least possible value of n?
原库参考解析
2023年12月D卷 · 原库模块 2 · Q14作答 ↗