What 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 is the nature of the roots of a quadratic equation with discriminant of 0?

When discriminant is equal to zero, the roots are equal and real.

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.

What is the nature of the roots of 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.

When the value of the discriminant is 0 the roots are?

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. In this case, we have two real roots. These values of x are the two distinct real roots of the given equation.

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

What happens when discriminant is 0?

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 of the quadratic equation 4m2 8m 9 0?

✰ Solution :-

∴ Quadratic equation have non - real roots.

What is the nature of roots of the quadratic equation 4x2 12x 9 0?

What is the nature of roots of the quadratic equation 4x² – 12x – 9 = 0? Since D > 0, therefore, roots of the given equation are real and unequal.

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

1 Answer. Hence, roots of the quadratic equation are real and unequal.

What is the nature of the roots of the quadratic equation whose discriminant is a perfect square?

Δ and nature of the roots:

(i) If Δ is a perfect square then the roots are rational and distinct. (ii) If Δ is not a perfect square then the roots are irrational and distinct. 2. If Δ = 0 then the roots are real and equal.

What is the nature of the root of the quadratic equation 2xsquare 3x 4 0?

Answer: The roots are real and distinct.

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.

What is the nature of roots of the equation 9x2 1 0?

so, the roots are imaginary.

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 of quadratic equation m2 2m 9 0?

Answer : The root of the equation are not real.

Which of the following is the value of discriminant for √ 2x2 5x+ √ 2 0?

Answer. the value of discriminant is 17.

For what value of k the roots of the quadratic equation 5x2 2kx 125 0 are real and equal?

Expert-verified answer

the value of a is 25 then the given equation has real and equal roots.

What is the nature of the roots of the quadratic equation if the value of its discriminant is greater than zero and a perfect square?

In this case, we say that the roots are imaginary. When a, b, and c are real numbers, a ≠ 0 and the discriminant is positive and perfect square, then the roots α and β of the quadratic equation ax² + bx + c = 0 are real, rational and unequal.

What are the roots of √ 121?

The square root of 121 is 11. The square root of a number is defined as a number, which when squared gives the original number. If 11 is multiplied twice, we get 121. Hence, the square root of 121 is 11.

What is nature of roots of quadratic equation?

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 best describes a quadratic equation with a discriminant of zero?

If the discriminant is 0, that means you have a 0 under the square root in the quadratic formula.

How many solutions are there if the discriminant is 0?

It tells you the number of solutions to a quadratic equation. If the discriminant is greater than zero, there are two solutions. If the discriminant is less than zero, there are no solutions and if the discriminant is equal to zero, there is one solution.

What is the value of 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.