# Difference between revisions of "2003 AMC 12A Problems/Problem 25"

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==Problem== | ==Problem== | ||

− | Let <math>\displaystyle f(x)= \sqrt{ax^2+bx} </math>. For how many real values of <math>a</math> is there at least one positive value of <math> b </math> for which the domain of <math>f </math> and the range <math> f </math> are the same set? | + | Let <math>\displaystyle f(x)= \sqrt{ax^2+bx} </math>. For how many [[real number | real]] values of <math>a</math> is there at least one [[positive number | positive]] value of <math> b </math> for which the [[domain]] of <math>f </math> and the [[range]] of <math> f </math> are the same [[set]]? |

<math> \mathrm{(A) \ 0 } \qquad \mathrm{(B) \ 1 } \qquad \mathrm{(C) \ 2 } \qquad \mathrm{(D) \ 3 } \qquad \mathrm{(E) \ \mathrm{infinitely \ many} } </math> | <math> \mathrm{(A) \ 0 } \qquad \mathrm{(B) \ 1 } \qquad \mathrm{(C) \ 2 } \qquad \mathrm{(D) \ 3 } \qquad \mathrm{(E) \ \mathrm{infinitely \ many} } </math> | ||

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==See Also== | ==See Also== | ||

*[[2003 AMC 12A Problems/Problem 24 | Previous problem]] | *[[2003 AMC 12A Problems/Problem 24 | Previous problem]] | ||

− | *[[2003 AMC 12A]] | + | *[[2003 AMC 12A Problems]] |

[[Category:Intermediate Algebra Problems]] | [[Category:Intermediate Algebra Problems]] |