AMC12 2002 A

AMC12 2002 A · Q1

AMC12 2002 A · Q1. It mainly tests Quadratic equations, Factoring.

Compute the sum of all the roots of $(2x+3)(x-4)+(2x+3)(x-6)=0$

计算方程 $(2x+3)(x-4)+(2x+3)(x-6)=0$ 的所有根之和。

(A) $\frac{7}{2}$ $\frac{7}{2}$

(B) 4 4

(D) 7 7

(E) 13 13

Answer

Correct choice: (A)

正确答案：（A）

Solution

We expand to get $2x^2-8x+3x-12+2x^2-12x+3x-18=0$ which is $4x^2-14x-30=0$ after combining like terms. Using the quadratic part of Vieta's Formulas, we find the sum of the roots is $\frac{14}4 = \boxed{\textbf{(A) }7/2}$.

展开得 $2x^2-8x+3x-12+2x^2-12x+3x-18=0$，合并同类项得 $4x^2-14x-30=0$。由韦达定理（二次项），根之和为 $\frac{14}4 = \boxed{\textbf{(A) }7/2}$。

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