What is -x^2+2x+3>= 0 ?

The solution to -x^2+2x+3>= 0 is -1<= x<= 3

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-x^2+2x+3>= 0

- x^{2} + 2 x + 3 \geq 0

- 1 \leq x \leq 3

Interval Notation

[- 1, 3]

Solution steps

- x^{2} + 2 x + 3 \geq 0

Factor

- x^{2} + 2 x + 3 : - (x + 1) (x - 3)

- (x + 1) (x - 3) \geq 0

Multiply both sides by

- 1

(reverse the inequality)

(- (x + 1) (x - 3)) (- 1) \leq 0 \cdot (- 1)

Simplify

(x + 1) (x - 3) \leq 0

Identify the intervals

- 1 \leq x \leq 3

\frac{1}{3} + \frac{1}{5} + \frac{1}{2}

x^{2} + 9 x + 6 = 0

x^{2} + 4 x + 4 > 0

3 u^{2} - 11 u = 4

- x^{2} = 6 x + 3