5272道题目5525 条题源记录 · 相同内容已合并
判别式・相切与根的个数挑战
\( x\left(kx-112\right)=-8 \)
In the given equation, k is an integer constant. If the equation has two distinct real solutions, what is the greatest possible value of k?
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判别式・相切与根的个数挑战
\( -x^2+bx-64=0 \)
In the given equation, b is an integer. The equation has no real solutions. What is the least possible value of b?
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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?
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判别式・相切与根的个数挑战
\( y=x-c \)
\( y=-4(x-6)^2 \)
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?
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判别式・相切与根的个数进阶
\( y=3x^2-24x+51 \)
\( y+4=0 \)
How many solutions are there to the given system of equations?
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判别式・相切与根的个数挑战
\( 81x^{2}+\frac{18}{33}x+ \)p\( =0 \)
In the given equation, p is a constant. The equation has exactly one real solution. What is the value of p?
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判别式・相切与根的个数挑战
\( nx^2-16x=26x^2-8 \)
In the given equation, n is an integer constant. If the equation has two distinct real solutions, what is the greatest possible value of n?
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判别式・相切与根的个数挑战
In the xy-plane, the graph of the equation \( y=-x^2+7x-76 \) intersects the line \( y=c \)at exactly one point. What is the value of c?
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判别式・相切与根的个数进阶
\( x^2+\left(\sqrt{k-3}\right)x+33=0 \)
In the given equation, k is a constant. The equation has exactly one real solution. What is the value of k?
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判别式・相切与根的个数进阶
\( x^2-\frac{81}{16}=0 \)
How many distinct real solutions does the given equation have?
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判别式・相切与根的个数挑战
\( x^2+\left(\sqrt{k-3}\right)x+42=0 \)
In the given equation, k is a constant. The equation has exactly one real solution. What is the value of k?
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判别式・相切与根的个数挑战
\( 9x^2+8=nx \)
In the given equation, n is a constant. The equation has exactly one solution. What is the value of \( \frac{n^2}{8} \)?
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