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# The discriminant

Consider the general quadratic equation ax2+bx+c=0. The quantity b2-4ac is called the discriminant of the quadratic equation and determine the type of root which arises from a quadratic equation. When
• b2-4ac > 0 The equation has two real roots.
• b2-4ac < 0 The equation has no real roots.
• b2-4ac = 0 The equation has one repeated root.

(If the discriminant is negative, the roots are complex, and this page can not display the complex number. The output will be "None").

Find the number of solutions of 3x2-2x=7
First write the equation in standard form: 3x2-2x-7=0
The discriminant is b2-4ac=(-2)2-4·3·(-7)=4+84=88>0
The equation has two real solutions.

How many roots does the following equation have? $\fs1-7x^2+8x-4\;=\;0$

None One Two