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 is the nature of the roots if the value of the discriminant is zero?

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.

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.

What is the nature of the quadratic equation if the discriminant is zero?

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.

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?

Clearly, the discriminant of the given quadratic equation is positive but not a perfect square. Therefore, the roots of the given quadratic equation are real, irrational and unequal.

How To Determine The Discriminant of a Quadratic Equation

What is the nature of the roots of the 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.

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.

What is the nature of solution if D 0?

Answer : If D = 0, then the two simultaneous equations do not have a unique solution.

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

Δ and nature of the roots:

If Δ > 0 then the roots are real and distinct. (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.

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 equation 9x2 1 0?

so, the roots are imaginary.

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

Answer: The roots are real and distinct.

Which of the following is the discriminant of the quadratic equation ax2 − bx c 0 where a/b/c are real numbers and a ≠ 0?

The discriminant of the quadratic equation ax2+bx+c=0 is Δ=b2−4ac.

Which of the following expressions Ggives us the discriminant of a quadratic equation ax 2 bx c 0ax 2 bx c 0?

In the Quadratic Formula, the expression underneath the radical symbol determines the number and type of solutions the formula will reveal. This expression, b² – 4ac, is called the discriminant of the equation ax² + bx + c = 0.

What is the nature of the of 0?

0 is the integer immediately preceding 1. Zero is an even number because it is divisible by 2 with no remainder. 0 is neither positive nor negative, or both positive and negative. Many definitions include 0 as a natural number, in which case it is the only natural number that is not positive.

When D 0 then both roots of quadratic equation will be?

Formulas for Solving Quadratic Equations

D = 0, roots are real and equal (coincident)

When D 0 then the roots are?

If D > 0, all the three roots are real and distinct. If D = 0, then all the three roots are real where at least two of them are equal to each other. If D < 0, then two of its roots are complex numbers and the third root is real.

What is the nature of roots of the quadratic equation 4x 2 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 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.

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.