How do you solve x^2 - 4x -3 = 0x24x3=0?

1 Answer
Aug 9, 2015

Use the quadratic formula to find x = 2+-sqrt(7)x=2±7

Explanation:

x^2-4x-3x24x3 is of the form ax^2+bx+cax2+bx+c, with a=1a=1, b=-4b=4 and c=-3c=3.

This has discriminant Delta given by the formula:

Delta = b^2-4ac = (-4)^2-(4xx1xx-3) = 16+12 = 28

= 2^2*7

This is positive but not a perfect square, so x^2-4x-3 = 0 has two distinct irrational roots.

Use the quadratic formula to give the roots:

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

= (4+-2sqrt(7))/2 = 2+-sqrt(7)