3x2−5x+7=0 is a quadratic equation. This can be solved in 3 ways: factorising, using the quadratic formula or by completing the square. It's not obvious how to factorise 3x2−5x+7=0 so we'll use the quadratic formula:
x=−b±√b2−4ac2a
a is the coefficient of x2, in this case 3.
b is the coefficient of x, in this case -5.
c is the constant, in this case 7.
Putting these values into the quadratic equation:
x=−(−5)±√(−5)2−4(3)(7)2(3)
x=5±√25−846
x=5±√−596
x=5±i√596
So the roots are:
x=5+i√596
and,
x=5−i√596
√−59 is an imaginary number, equal to √−1√59, which equals i√59. The symbol for the square root of -1 is i. Thus the roots of this equation have a real part (the 5/6) and an imaginary part (the ±i√596). A number made up of a real and imaginary part is called a complex number. Hence there are no real roots to this quadratic, which means it does not cross the x-axis.
