What is the discriminant of #5x^2-8x-3=0# and what does that mean?

1 Answer
Jul 24, 2015

Answer:

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=124#

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;

#5x^2−8x−3=0#

Now compare the above equation with quadratic equation #ax^2+bx+c=0#, we get #a=5, b=-8 and c = -3#.

Hence the discriminant (D) is given by;

#D = b^2-4ac#
#=> D = (-8)^2 - 4*5*(-3)#
#=> D = 64-(-60)#
#=> D = 64+60=124#

Therefore the discriminant of a given equation is 124.

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.

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