Question

Help trig question involving discriminant?

a)Find the value of the discriminant.
b)Use any method to find the real roots of the equation if they exist.

2x^2+7x=0

Answer 1

surely you got as far as evaluating the discriminant: b^2 - 4ac = 7 - 0 = 7

factor: x(2x+7) = 0

a product is zero if any factor is zero. So,

x=0 or (2x+7) = 0
so, the roots are 0 and -7/2

Using the quadratic formula, we have

x = [-7 +/- sqrt(49-0)]/4
= [-7 +/- 7]/2
= 0 or -7/2

Completing the square,

2(x^2 + 7/2 x + (7/4)^2) - 2(7/4)^2 = 0
2(x + 7/4)^2 = 2(7/4)^2
x + 7/4 = (7/4)^2 = 49/16

x = -7/4 +/- 7/4
= 0 or -7/2