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二次方程・零点与韦达定理进阶

x - 29 = (x - a)(x - 29)
Which of the following are solutions to the given equation, where a is a constant and a > 30?
I. a
II. a+ 1
II. 29
原库参考解析
Bluebook试题3 · 原库模块 1 · Q22作答 ↗
二次方程・零点与韦达定理进阶

y = 76
y = x2 - 5
The graphs of the given equations in the xy-plane intersect at the point (x, y). What is a possible value of x?
原库参考解析
Bluebook试题3 · 原库模块 1 · Q7作答 ↗
二次方程・零点与韦达定理基础

The function g is defined by g(x)= x2 + 9. For which value of x is g(x) = 25?
原库参考解析
Bluebook试题3 · 原库模块 2 · Q6作答 ↗
二次方程・零点与韦达定理挑战

x2 - 2x - 9 = 0
One solution to the given equation can be written as 1 + 根號 k, where k is a constant. What is the value of k?
原库参考解析
Bluebook试题3 · 原库模块 3 · Q19作答 ↗
二次方程・零点与韦达定理挑战

57x2 + (57b + a)x + ab = 0
In the given equation, a and b are positive constants. The product of the solutions to the given equation is kab, where k is a constant. What is the value of k?
原库参考解析
Bluebook试题4 · 原库模块 3 · Q19作答 ↗
二次方程・零点与韦达定理进阶

(d-30)(d+30)-7=-7
What is a solution to the given equation?

原库参考解析
Bluebook试题5 · 原库模块 1 · Q11作答 ↗
二次方程・零点与韦达定理挑战

\( y=x+9 \) 
\( y=x^2+16x+63 \) 
A solution to the given system of equations is (x, y). What is the greatest possible value of x?

原库参考解析
Bluebook试题5 · 原库模块 2 · Q9作答 ↗
二次方程・零点与韦达定理基础

\( y=4x \) 
\( y=x^2-12 \) 

A solution to the given system of equations is (\( x,\ y \)), where \( x \) > 0. What is the value of \( x \)?
原库参考解析
Bluebook试题5 · 原库模块 3 · Q18作答 ↗
二次方程・零点与韦达定理进阶

The function g is defined by g(x)=(x + 14)( t - x), where t is a constant. In the xy-plane, the graph of y= g(x) passes through the point (24, 0). What is the value of g(0)?
原库参考解析
Bluebook试题6 · 原库模块 1 · Q20作答 ↗
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(x) in the xy-plane passes through the points (7, 0) and (-3, 0). If a is an integer greater than l, which of the following could be the value of a + b?
原库参考解析
Bluebook试题6 · 原库模块 2 · Q22作答 ↗
二次方程・零点与韦达定理挑战

\( w^2+12w-40=0 \) 
Which of the following is a solution to the given equation?
原库参考解析
Bluebook试题6 · 原库模块 2 · Q9作答 ↗
二次方程・零点与韦达定理基础

\( k^2-53=91 \) 
What is the positive solution to the given equation?

原库参考解析
Bluebook试题6 · 原库模块 3 · Q8作答 ↗