Determine the number of roots, using the most efficient method possible. a) y = -5(x + 1)2 - 3 b) y = 2(x - 1)(x + 3) c) y = 2x2 + 3x + 1

2 roots in every case, not all are real.

Step-by-step explanation:

All of these equations are quadratic equations (degree 2). Every quadratic has two roots. They may be identical (looks like 1 root), and they may be complex (zero real roots), but there are always 2 of them.

a) the y-value of the vertex is negative and the parabola opens downward (leading coefficient -5), so there are no real zeros and both roots are complex.

b) each binomial factor contributes a root. Both roots are real.

c) the discriminant is positive, (3²-4·2·1=1), so both roots are real.

560

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