Which of the following is the nature 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 positive and a perfect square?

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.

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.

What are the roots if the discriminant is negative?

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

What is the nature of the roots of quadratic equation if the value of the discriminant is 49?

If the discriminant is a perfect square, such as 49 or 100, then the roots will be rational (fractional) numbers.

How To Determine The Discriminant of a Quadratic Equation

What are the nature of the roots of a 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 of a quadratic equation if the value of its discriminant is less than zero?

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 the roots of the discriminant is?

The discriminant is defined as Δ=b2−4ac. This is the expression under the square root in the quadratic formula. 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 happens when the discriminant is greater than 0?

When the discriminant is greater than 0, there are two distinct real roots. When the discriminant is equal to 0, there is exactly one real root. When the discriminant is less than zero, there are no real roots, but there are exactly two distinct imaginary roots.

Are roots rational or irrational?

Sal proves that the square root of any prime number must be an irrational number. For example, because of this proof we can quickly determine that √3, √5, √7, or √11 are irrational numbers.

What is the nature of the roots of quadratic equation ax2 bx c 0 if b2 4ac 0?

Clearly, −b2a is a real number because b and a are real. Thus, the roots of the equation ax2 + bx + c = 0 are real and equal if b2 – 4ac = 0.

What is the nature of the roots?

Nature of Roots Calculator

The curve of the quadratic equation is in the form of a parabola. The quadratic formula is given by −b±√b2−4ac2a − b ± b 2 − 4 a c 2 a . The discriminant is given by b2−4ac b 2 − 4 a c . This is used to determine the nature of the roots of a quadratic equation.

When the discriminant of a quadratic equation is 0 it means?

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.

When the discriminant of a quadratic equation is less than zero there are is?

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 discriminant of a quadratic equation is greater than zero?

If the discriminant is greater than zero, this means that the quadratic equation has two real, distinct (different) roots. x² - 5x + 2. If the discriminant is greater than zero, this means that the quadratic equation has no real roots.

What is the nature of roots of a quadratic equation with discriminant of 12?

If the discriminant of a quadratic equation is 12 , then it has two distinct real roots. Note that 12 is not a perfect square, so if the coefficients of the quadratic are integers or otherwise rational, then the roots are both irrational.

What will be the nature of roots of quadratic equation 2x 2 7x 4 0?

Hence, root of quadratic equation are real and unequal.

What is the nature of the roots of the quadratic equation 4x² 8x 9 0?

Answer. The roots are imaginary because roots cannot be negative .

What is the nature of roots of the quadratic equation 2x2 √ 5x 1 0?

Hence, the roots of the quadratic equation 2x² – √5x + 1 = 0 are imaginary.

What is the nature of the roots of the quadratic equation when B² 4ac is negative?

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 a quadratic equation with a discriminant of 144?

Because the discriminant is 144>0, there are two real roots.

Which of the following is the discriminant of the quadratic equation ax2 bx c 0?

In the case of a quadratic equation ax² + bx + c = 0, the discriminant is b² − 4ac; for a cubic equation x³ + ax² + bx + c = 0, the discriminant is a²b² + 18abc − 4b³ − 4a³c − 27c².

What are the roots of quadratic equation ax2 bx c 0?

We know that the roots of the quadratic equation ax² + bx + c = 0 by quadratic formula are (-b + √ (b² - 4ac) )/2a and (-b - √ (b² - 4ac) )/2a.