Question

设 $d$ 和 $e$ 是方程 $2x^2 + 3x - 5 = 0$ 的解。求 $(d - 1)(e - 1)$ ？

Let $d$ and $e$ denote the solutions of $2x^2 + 3x - 5 = 0.$ What is the value of $(d - 1)(e - 1)?$

$-\dfrac{5}{2}$

$0$

$3$

$5$

$6$

因式分解得 $2x^2 + 3x - 5 = (2x + 5)(x - 1)$ ，所以两个根为 $-\dfrac{5}{2}$ 和 $1$ 。

因为一个根等于 $1$ ，所以相应因子 $(e - 1) = 0$ ，乘积为 $0$ 。

所以正确答案是 B。

Factoring gives $2x^2 + 3x - 5 = (2x + 5)(x - 1),$ so the roots are $-\dfrac{5}{2}$ and $1.$

Since one root equals $1,$ the factor $(e - 1) = 0,$ making the product $0.$

Thus, the correct answer is B.