which of the following mathematical statements is a quadratic inequality?a)5t^2-r-20=0
b)9h+18<0
c)4x^2+2x-2>=0
d)m^2+9m+16=0
Which mathematical statement is a quadratic inequality in one wariable
To determine which of the given mathematical statements is a quadratic inequality, we need to understand what a quadratic inequality is.
A quadratic inequality is an inequality that involves a quadratic expression, which is a polynomial of degree 2. It can be written in the form ax^2 + bx + c > 0, ax^2 + bx + c < 0, ax^2 + bx + c ≥ 0, or ax^2 + bx + c ≤ 0, where a, b, and c are real numbers.
Now let's analyze the options:
a) 5t^2 - r - 20 = 0: This is a quadratic equation, not a quadratic inequality, as it is set equal to zero.
b) 9h + 18 < 0: This is a linear inequality, as it only involves a linear expression. It is not a quadratic inequality.
c) 4x^2 + 2x - 2 ≥ 0: This is a quadratic inequality as it involves a quadratic expression (4x^2 + 2x - 2) and is greater than or equal to zero.
d) m^2 + 9m + 16 = 0: This is also a quadratic equation, not a quadratic inequality, as it is set equal to zero.
Therefore, the correct answer is option c) 4x^2 + 2x - 2 ≥ 0.