Trigonometry
posted by Tomtom .
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

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(490)]/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
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