What is the discriminant of 0=3x^2-4x-3 and what does that mean?

1 Answer
Anwar Hussain
Jul 24, 2015

The discriminant of an equation tells the nature of the roots of a quadratic equation given that a,b and c are rational numbers.

D=52

Explanation:

The discriminant of a quadratic equation ax^2+bx+c=0 is given by the formula b^2+4ac of the quadratic formula;

x = (-b+-sqrt{b^2-4ac})/(2a)

The discriminant actually tells you the nature of the roots of a quadratic equation or in other words, the number of x-intercepts, associated with a quadratic equation.

Now we have an equation;

0=3x^2−4x−3
3x^2−4x−3=0

Now compare the above equation with quadratic equation ax^2+bx+c=0, we get a=3, b=-4 and c = -3.

Hence the discriminant (D) is given by;

D = b^2-4ac
=> D = (-4)^2 - 4*3*(-3)
=> D = 16-(-36)
=> D = 16+36=52

Therefore the discriminant of a given equation is 52.

Here the discriminant is greater than 0 i.e. b^2-4ac>0, hence there are two real roots.

Note: If the discriminant is a perfect square, the two roots are rational numbers. If the discriminant is not a perfect square, the two roots are irrational numbers containing a radical.

Thanks

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