SAT Math · Equivalent expressions · medium

What is the product of the two solutions to x² + 3x - 40 = 0?

What is the product of the two solutions to x2+3x−40=0x^2 + 3x - 40 = 0?

Answer and explanation

Answer: A: -40

Factor: x2+3x−40=(x+8)(x−5)x^2 + 3x - 40 = (x + 8)(x - 5), since 8⋅(−5)=−408 \cdot (-5) = -40 and 8+(−5)=38 + (-5) = 3. The solutions are x=−8x = -8 and x=5x = 5, and their product is −8×5=−40-8 \times 5 = -40, choice A. By Vieta's formulas, the product of the roots equals the constant term, so you can read −40-40 straight from the equation. Choice B (40) drops the sign. Choice C (3) is the xx-coefficient, and choice D (−3-3) is the sum of the roots, −8+5-8 + 5. The product of the roots is the constant term, and the sum is the opposite of the xx-coefficient.

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