Which of the following will determine the nature of the roots of a quadratic equation?

The discriminant determines the nature of the roots of a quadratic equation. The word 'nature' refers to the types of numbers the roots can be — namely real, rational, irrational or imaginary.

Which of the following is the nature of the roots of the roots of the quadratic equation if the value of its discriminant is negative?

If the discriminant of the quadratic equation is negative, then the square root of the discriminant will be undefined.

Which of the following is the nature of the roots of the quadratic equation if the value of its discriminant is zero?

Answer : If the value of the discriminant is 0, the roots of a quadratic equation are real and equal.

Which of the following is the nature of the roots of the quadratic equation if the value of its discriminant is positive and not a perfect square?

When a, b, and c are real numbers, a ≠ 0 and the discriminant is positive but not a perfect square then the roots of the quadratic equation ax² + bx + c = 0 are real, irrational and unequal.

How important is the discriminant in determining the nature of roots of quadratic equations?

The discriminant is actually part of the quadratic formula. It is super useful when we only need to determine whether a quadratic equation has 2 real solutions, 1 real solution, or 2 complex solutions.

Nature of Roots - Examples | Quadratic Equations | Don't Memorise

What are the types of different nature of roots of quadratic equation?

The discriminant determines the nature of the roots of a quadratic equation. The word 'nature' refers to the types of numbers the roots can be — namely real, rational, irrational or imaginary.

What is 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.

Which of the following is quadratic equation?

The standard form of a quadratic is y = ax^2 + bx + c, where a, b, and c are numbers and a cannot be 0. Examples of quadratic equations include all of these: y = x^2 + 3x + 1. y = x^2.

What do you mean by nature of quadratic equation?

We already know what a quadratic equation is, let us now focus on nature of roots of quadratic equation. A polynomial equation whose degree is 2, is known as quadratic equation. A quadratic equation in its standard form is represented as: a x 2 + b x + c.

How do you find the nature of the roots Class 10?

Where D = √b² − 4ac is called the discriminant. This formula is known as the Quadratic Formula. The nature of the roots depends upon the value of Discriminant, D. The given quadratic equation is x² − 4x − 5 = 0.

What are the two natures of roots?

There are three types of roots : Complex roots. Real and equal roots. Real and Distinct roots.

When the discriminant is negative then the nature of the roots are?

If the discriminant b2−4ac of a quadratic equation is negative, then its roots are imaginary.

What are roots in a quadratic function?

Roots are also called x-intercepts or zeros. A quadratic function is graphically represented by a parabola with vertex located at the origin, below the x-axis, or above the x-axis. Therefore, a quadratic function may have one, two, or zero roots.

Which of the following quadratic equation has no real roots?

Solution: A quadratic equation ax² + bx + c = 0 has no real roots if discriminant < 0. Hence option A is the answer.

Which of the following is a quadratic equation class 10th?

x2−3x+5=0.

Which of the following is not a quadratic equation?

option B is a linear equation, not a quadratic equation.

Why does the discriminant determine the number of solutions?

The discriminant is the term underneath the square root in the quadratic formula and tells us the number of solutions to a quadratic equation. If the discriminant is positive, we know that we have 2 solutions. If it is negative, there are no solutions and if the discriminant is equal to zero, we have one solution.