MathDB
Coefficient Switcharoo

Source: 2021 AMC 12A #17, AMC 10A #20

November 11, 2021
2021 amc 12aAMCAMC 12AMC 12 A

Problem Statement

How many ordered pairs of positive integers (b,c)(b,c) exist where both x2+bx+c=0x^2+bx+c=0 and x2+cx+b=0x^2+cx+b=0 do not have distinct, real solutions?
<spanclass=latexbold>(A)</span>4<spanclass=latexbold>(B)</span>6<spanclass=latexbold>(C)</span>8<spanclass=latexbold>(D)</span>10<spanclass=latexbold>(E)</span>12<span class='latex-bold'>(A) </span> 4 \qquad <span class='latex-bold'>(B) </span> 6 \qquad <span class='latex-bold'>(C) </span> 8 \qquad <span class='latex-bold'>(D) </span> 10 \qquad <span class='latex-bold'>(E) </span> 12 \qquad