2003 AMC 10A Problem 5

Problem 5 of 25EasierAlgebra

Let

d

and

e

denote the solutions of

2x^2 + 3x - 5 = 0.

What is the value of

(d - 1)(e - 1)?

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Solution

Factoring gives

2x^2 + 3x - 5 = (2x + 5)(x - 1),

so the roots are

-\dfrac{5}{2}

and

1.

Since one root equals

1,

one of the two factors

d-1

and

e-1

equals

0,

making the product

0.

Thus, the correct answer is B.

Concepts: quadratic · factoring

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