What is the product of the 2 solutions of the equation #x^2+3x-21=0#?

1 Answer
Shwetank Mauria
Apr 6, 2017

Product of the two solutions is #-21#.

Explanation:

If we have a quadratic equation #ax^2+bx+c=0#

sum of the two solutions is #-b/a# and product of the two solutions is #c/a#.

In the equation, #x^2+3x-21=0#,

sum of the two solutions is #-3/1=-3# and product of the two solutions is #-21/1=-21#.

Note that as discriminant #b^2-4ac=3^2-4xx1xx(-21)=9+84=93# is not a square of a rational number, the two solutions are irrational numbers. These are given by quadratic formula

#(-b+-sqrt(b^2-4ac))/(2a)# and for #x^2+3x-21=0#, these are

#(-3+-sqrt93)/2# i.e. #-3/2+sqrt93/2# and #-3/2-sqrt93/2#

One can check as product of #-3/2+sqrt93/2# and #-3/2-sqrt93/2# is

#(-3/2)^2-(sqrt93/2)^2=9/4-93/4=-84/4=-21#

Related questions
Impact of this question
22477 views around the world
You can reuse this answer
Creative Commons License