5272道题目5525 条题源记录 · 相同内容已合并
判别式・相切与根的个数进阶
The quadratic equation \( (2x-64)^2=a \), where a is a constant, has exactly one real solution. What is the value of a?
原库参考解析
判别式・相切与根的个数挑战
\( r^2+qr=8r-87 \)
In the given equation, q is an integer constant. The given equation has no real solutions. What is the largest possible value of q?
原库参考解析
判别式・相切与根的个数挑战
\( 2x^2=k \)
In the given the equation, k is a constant. The equation has no real solution. Which of the following could be the value of k ?
原库参考解析
判别式・相切与根的个数基础
\( 3x^2−13x+19=0 \)
How many distinct real solutions does the given equation have?
原库参考解析
判别式・相切与根的个数挑战
\( -6x^2+bx-96=0 \)
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
判别式・相切与根的个数挑战
\( y=3x^2+28 \)
\( y=px+25 \)
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?
原库参考解析
判别式・相切与根的个数挑战
\( -3x^2+bx-48=0 \)
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
判别式・相切与根的个数挑战
The quadratic equation \( (2x-36)^2=a \), where a is a constant, has exactly one real solution. What is the value of a?
参考答案
判别式・相切与根的个数进阶
The quadratic equation \( (7x-64)^2=a \), where a is a constant, has exactly one real solution. What is the value of a?
参考答案
判别式・相切与根的个数挑战
\( 9x(x+5)=r \)
In the given equation, r is a positive constant. Which of the following must be true?
参考答案
判别式・相切与根的个数挑战
\( x^2+(\sqrt{k-3})x+42=0 \)
In the given equation, k is a constant. The equation has exactly one real solution. What is the value of k ?
参考答案
判别式・相切与根的个数挑战
\( 6x^2+11=nx \)
In the given equation, n is a constant. The equation has exactly one solution. What is the value of \( \frac{n^2}{8} \)?
参考答案
