What is the discriminant of 5x2−8x−3=0 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=124

Explanation:

The discriminant of a quadratic equation ax2+bx+c=0 is given by the formula b2+4ac of the quadratic formula;

x=−b±√b2−4ac2a

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;

5x2−8x−3=0

Now compare the above equation with quadratic equation ax2+bx+c=0, we get a=5,b=−8andc=−3.

Hence the discriminant (D) is given by;

D=b2−4ac
⇒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. b2−4ac>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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