Question

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How many REAL number solutions does the equation 7x2 - 5x + 1 = 0 have?

Answer 1

\[7x^2-5x+1=0\]is a quadratic of the form \[ax^2+bx+c=0\]The discriminant \(\Delta = b^2-4ac\) will characterize the solutions:
If \(\Delta = 0\), a perfect square with 1 real solution
if \(\Delta > 0\), two real roots
if \(\Delta < 0\), two complex roots in a conjugate pair \((a\pm bi)\)