SOLUTION: decide all values of b in the following equations that will give one or more real number solutions. (a) 3x^2 + bx - 3 = 0 (b) 5x^2 + bx + 1 = 0 (c) -3x^2 + bx

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Question 102279: decide all values of b in the following equations that will
give one or more real number solutions.
(a) 3x^2 + bx - 3 = 0
(b) 5x^2 + bx + 1 = 0
(c) -3x^2 + bx - 3 = 0
Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
decide all values of b in the following equations that will
give one or more real number solutions.
(a) 3x^2 + bx - 3 = 0
(b) 5x^2 + bx + 1 = 0
(c) -3x^2 + bx - 3 = 0
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Each of these is a quadratic equation.
To have Real Number solutions the discriminant must be > or = to zero.
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a) a=3,b=b,c=-3
b^2-4ac>=0
b^2-4*3*-3>=0
b^2+36 >=0
b^2 >= -36
But b^2 is always >= -36 so b may have any Real Number value.
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Follow the same procedure on questions b) and c).
Cheers,
Stan H.

Answer by MathLover1(20850) (Show Source):
You can put this solution on YOUR website!
In the standard form

the roots are:
if

then the roots are . Otherwise, the roots are
So
(a)

the roots are for any vale of
(b)

the roots are for any vale of
(c)

the roots are for any value of

SOLUTION: decide all values of b in the following equations that will give one or more real number solutions. (a) 3x^2 + bx - 3 = 0 (b) 5x^2 + bx + 1 = 0 (c) -3x^2 + bx - 3 = 0