What is required to give two distinct real roots?

For the quadratic equation ax2 + bx + c = 0, the expression b2 – 4ac is called the discriminant. The value of the discriminant shows how many roots f(x) has: – If b2 – 4ac > 0 then the quadratic function has two distinct real roots. – If b2 – 4ac < 0 then the quadratic function has no real roots.

What is the condition for real and distinct roots?

If an equation has real roots, then the solutions or roots of the equation belongs to the set of real numbers. If the equation has distinct roots, then we say that all the solutions or roots of the equations are not equal. When a quadratic equation has a discriminant greater than 0, then it has real and distinct roots.

What does 2 distinct real roots mean?

If any two roots of it are not equal and belong to the set of real numbers. They are said to be distinct real roots.

How do you know if an equation has no real roots?

Case 1: No Real Roots If the discriminant of a quadratic function is less than zero, that function has no real roots, and the parabola it represents does not intersect the x-axis.

What is the meaning of distinct in maths?

In math, the term distinct number is used to refer to a number in a set that is not equal to another number. For example, the set of numbers {1, 2} contains the two distinct numbers 1 and 2, which can be proven by evaluating different traits of each number.

What is a distinct zero?

Distinct zeros mean different values of x. Getting to the Answer: You are looking for the graph that has four different x-intercepts, or in other words, crosses through the x-axis four times, which is the graph in (D). Note that the graphs in A and C have two distinct zeros, and the graph in B has three.

What are real roots?

Given an equation in a single variable, a root is a value that can be substituted for the variable in order that the equation holds. In other words it is a “solution” of the equation. It is called a real root if it is also a real number. For example: x2−2=0.

What is a distinct real zero?

A positive discriminant indicates that the quadratic has two distinct real number solutions. A discriminant of zero indicates that the quadratic has a repeated real number solution. A negative discriminant indicates that neither of the solutions are real numbers.