5272道题目5525 条题源记录 · 相同内容已合并
二次方程・零点与韦达定理挑战
\( x^2+5x=37 \)
The solutions to the given equation are \( \frac{m+\sqrt{q}}{2} \) and \( \frac{m-\sqrt{q}}{2} \) , where m and q are integers. What is the value of \( m+q \) ?
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二次方程・零点与韦达定理挑战
\( 3x^2+x-5=0 \)
What is the greatest solution to the given equation?
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二次方程・零点与韦达定理挑战
\( 33x^2+\left(33s+r\right)x+rs=0 \)
In the given equation, r and s are positive constants. The product of the solutions to the given equation is krs, where k is a constant. What is the value of k?
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二次方程・零点与韦达定理挑战
x ( x +11) - 7 = 0
What are the solutions to the given equation?
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二次方程・零点与韦达定理挑战
\( f\left(x\right)=\left(x-a\right)\left(x-b\right) \)
The function \( f \) is defined by the given equation, where a and b are integer constants. If \( f(37)>0, \)\( f(40)<0 \)，and \( f(43)>0 \). What is one possible value of a + b?
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二次方程・零点与韦达定理挑战
The length of one side of a rectangle is 10 units longer than the length of another side. The rectangle's area is 504 square units. What is the length, in units, of the shorter of these two sides?
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二次方程・零点与韦达定理挑战
\( y-x=32 \)
\( y=x^2-30x \)
The graphs of the equations in the given system intersect at the point (x, y) in the xy-plane. What is a possible value of y?
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二次方程・零点与韦达定理挑战
If \( 121x^2=-110x+56 \) , what is the value of \( 11x+5 \), where \( 11x+5>0 \)?
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二次方程・零点与韦达定理挑战
\( x^2-5x-36=0 \)
What is the sum of the solutions to the given equation?
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二次方程・零点与韦达定理挑战
The function f is defined by \( f\left(x\right)=ax^2+bx+c \) , where a , b, and c are constants. The graph of \( y=f\left(x\right) \) in the xy-plane passes through the points \( \left(8,\ 0\right) \) and \( \left(-2,\ 0\right) \). If a is an integer greater than 1, which of the following could be the value of \( a+b \)?
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二次方程・零点与韦达定理挑战
\( 2x^2-12x-13=0 \)
One solution to the given equation can be written as \( x=h-\frac{1}{2}\sqrt{k} \) , where h and k are integer constants. What is the value of h + k?
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二次方程・零点与韦达定理进阶
The graph of a system of a linear equation and a quadratic equation is shown. A solution to the system is (x, y). What is a possible value of x?
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