What does it mean if the discriminant is negative?

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.

What is the nature of the roots if the discriminant is a negative number or is less than zero?

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When discriminant is greater than zero, the roots are unequal and real. When discriminant is equal to zero, the roots are equal and real. When discriminant is less than zero, the roots are imaginary.

What is the nature of roots in a discriminant?

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. Δ is the Greek symbol for the letter D. If Δ<0, then roots are imaginary (non-real) and beyond the scope of this book.

What will be the nature of the roots of the quadratic equation if the value of its discriminant is a perfect square positive number?

Clearly, the discriminant of the given quadratic equation is positive and a perfect square. Therefore, the roots of the given quadratic equation are real, rational and unequal.

How many roots does a negative discriminant have?

If the discriminant is positive, then you have , which leads to two real number answers. If it’s negative, you have , which gives two complex results. And if b2 – 4ac is 0, then you have , so you have only one solution.

What are the nature of roots of quadratic equation?

We can see, the discriminant of the given quadratic equation is positive but not a perfect square. Hence, the roots of a quadratic equation are real, unequal and irrational.

What is the nature of the roots if the discriminant of the quadratic equation is a negative number?

If the discriminant of the quadratic equation is negative, then the square root of the discriminant will be undefined. However, the square of a negative quantity can be expressed by an imaginary quantity. Now, the zeros or roots of the quadratic equation can be written in the following form.

What is the nature of the roots of the quadratic equation when b2 4ac is negative?

(ii) If b2 – 4ac is positive but not perfect square, the roots are irrational and unequal. If D = 0, i.e., b2 – 4ac = 0; the roots are real and equal. If D < 0, i.e., b2 – 4ac < 0; i.e., b2 – 4ac is negative; the roots are not real, i.e., the roots are imaginary.

What is the nature of the roots of quadratic equation if the value of the discriminant is negative?

If the discriminant of the quadratic equation is negative, then the square root of the discriminant will be undefined. However, the square of a negative quantity can be expressed by an imaginary quantity.

What is the nature of the roots of the quadratic equation *?

What is the relationship between discriminant and roots?

The relationship between discriminant and roots can be understood from the following cases – Then, the roots of the quadratic equation are real and unequal. Then, the roots of the quadratic equation are real and equal. Then, the roots of the quadratic equation are not real and unequal.

What is a positive and negative quadratic discriminant?

Answer: A positive discriminant denotes that the quadratic has two different real number solutions. A discriminant of zero denotes that the quadratic consists of a repeated real number solution. A negative discriminant denotes that neither of the solutions is real numbers. Question 3: What is a negative quadratic?

What does it mean when the discriminant is zero?

When discriminant is zero, it shows that there are repeated real number solution to the quadratic; For a negative discriminant, neither of the solutions amount to real numbers; For a positive discriminant, there are two distinct real number solutions to the quadratic equation.

What is the nature of roots in math?

Nature Of Roots. When a, b, and c are real numbers, a ≠ 0 and discriminant is positive, then the roots α and β of the quadratic equation ax 2 +bx+ c = 0 are real and unequal. When a, b, and c are real numbers, a ≠ 0 and discriminant is zero, then the roots α and β of the quadratic equation ax 2+ bx + c = 0 are real and equal.