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判别式・相切与根的个数挑战

x(kx - 56) = -16
In the given equation, k is an integer constant. If the equation has no real solution, what is the least possible value of k?
原库参考解析
Bluebook试题3 · 原库模块 3 · Q20作答 ↗
判别式・相切与根的个数基础

5x2 + 10x + 16 = 0
How many distinct real solutions does the given equation have?
原库参考解析
Bluebook试题4 · 原库模块 2 · Q21作答 ↗
判别式・相切与根的个数挑战

x2 - 34x + 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
Bluebook试题4 · 原库模块 3 · Q13作答 ↗
判别式・相切与根的个数挑战

Which quadratic equation has no real solutions?
原库参考解析
Bluebook试题5 · 原库模块 2 · Q13作答 ↗
判别式・相切与根的个数进阶

\( x^2=-841 \) 
How many distinct real solutions does the given equation have?

原库参考解析
Bluebook试题6 · 原库模块 1 · Q13作答 ↗
判别式・相切与根的个数挑战

\( -9x^2+30x+c=0 \) 
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
Bluebook试题8 · 原库模块 3 · Q14作答 ↗
判别式・相切与根的个数挑战

In the xy-plane, the graph of the equation \( y=-x^2+9x-100 \) intersects the line \( y=c \) at exactly one point. What is the value of \( c \) ?
原库参考解析
Bluebook试题9 · 原库模块 3 · Q19作答 ↗
判别式・相切与根的个数挑战

-x2 + bx  -676 = 0

In the given equation, b is a positive integer. The equation has no real solution. What is the greatest possible value of b ?
原库参考解析
one variable and systems of equations in two variables · 原库模块 1 · Q11作答 ↗
判别式・相切与根的个数挑战

2x2 - 4x  = t 

In the equation above, t is a constant. If the equation has no real solutions, which of the following could be the value of t ?
原库参考解析
one variable and systems of equations in two variables · 原库模块 1 · Q13作答 ↗
判别式・相切与根的个数挑战

x2 - 34x  + 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
one variable and systems of equations in two variables · 原库模块 1 · Q18作答 ↗
判别式・相切与根的个数挑战

-16x2 - 8x  + 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
one variable and systems of equations in two variables · 原库模块 1 · Q19作答 ↗
判别式・相切与根的个数挑战

(x -1)2 =-4
How many distinct real solutions does the given equation have?
原库参考解析
one variable and systems of equations in two variables · 原库模块 1 · Q20作答 ↗