Question 744036
When the equation has the form
{{{ ax^2 + b*x + c }}} , then the roots are found
using the quadratic formula:
{{{ x = (-b +- sqrt( b^2 - 4*a*c )) / (2*a) }}}
The discriminant is:
{{{ b^2 - 4a*c }}}
If the discriminant is positive, both roots are real
If the discriminant is negative, both roots are imaginary
If the discriminant is zero, there is 1 real root
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Your equation is:
{{{ 10z^2 + 3z - 3 = 0 }}}
{{{ a = 10 }}}
{{{ b = 3 }}}
{{{ c = -3 }}}
and the discriminant is:
{{{ b^2 - 4*a*c = 3^2 - 4*10*(-3) }}}
{{{ b^2 - 4*a*c = 9 + 120 }}}
{{{ b^2 - 4*a*c = 129 }}}
This result is positive, so there are 2 real roots
Here is the plot:
{{{ graph( 400, 400, -3, 3, -5, 5, 10x^2 + 3x - 3 ) }}}