What is quadratic inequality?
A quadratic inequality is an equation of second degree that uses an inequality sign instead of an equal sign. Examples of quadratic inequalities are: x2 – 6x – 16 ≤ 0, 2×2 – 11x + 12 > 0, x2 + 4 > 0, x2 – 3x + 2 ≤ 0 etc. Solving a quadratic inequality in Algebra is similar to solving a quadratic equation.
What is a discriminant in quadratic equation?
The discriminant is the part of the quadratic formula underneath the square root symbol: b²-4ac. The discriminant tells us whether there are two solutions, one solution, or no solutions.
What is quadratic and not quadratic?
A non-monic quadratic equation is an equation of the form ax2 + bx + c = 0, where and are given numbers, and a ≠ 1 or 0.
How do you describe quadratic equation?
noun Mathematics. an equation containing a single variable of degree 2. Its general form is ax2 + bx + c = 0, where x is the variable and a, b, and c are constants (a ≠ 0).
How do you describe quadratic inequalities in two variables?
A quadratic inequality in two variables represents a region of the Cartesian plane with a parabola as the boundary. The graph of a quadratic inequality is the set of points ( , )that are solutions to the inequality. We can use test points but it’s much easier to look at where the area contains the -axis.
What is quadratic equation and inequalities?
A quadratic equation is in standard form when written as ax2+bx+c=0. A quadratic inequality is an inequality that contains a quadratic expression. The standard form of a quadratic inequality is written: ax2+bx+c<0ax2+bx+c≤0ax2+bx+c>0ax2+bx+c≥0. The graph of a quadratic function f(x)=ax2+bx+c=0 is a parabola.
What does the value of the discriminant mean?
The discriminant tells you how many solutions there are to quadratic equation or how many x intercepts there are for a parabola. It tells you the number of solutions to a quadratic equation. If the discriminant is greater than zero, there are two solutions.
What is discriminant in quadratic equation class 10?
Discriminant. For a quadratic equation of the form ax2+bx+c=0, the expression b2−4ac is called the discriminant, (denoted by D), of the quadratic equation. The discriminant determines the nature of roots of the quadratic equation based on the coefficients of the quadratic equation.
Why quadratic equation is called quadratic?
We use the word quadratic because “quadra” refers to a square, and the leading term in a quadratic equation is “squared.” This is consistent with calling a degree three polynomial a “cubic” for the leading term represents a cube. The word for an equation with a leading term of x^4 is “quartic.”
How does quadratic inequalities differ from quadratic equations?
In algebra, solving a quadratic inequality is very similar to solving a quadratic equation. The difference is that with quadratic equations, you set the expressions equal to zero, but with inequalities, you’re interested in what’s on either side of the zero (positives and negatives).