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

Nature of Roots of a Quadratic Equation:

is defined and is a positive quantity. , we can never write it as a product of two equal quantities.

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

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 the quadratic equation in 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 nature of the roots of the quadratic equation using discriminant?

The discriminant (EMBFQ)

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.

Are roots rational or irrational?

Many square roots are irrational numbers, meaning there is no rational number equivalent. For example, 2 is the square root of 4 because \begin{align*}2 \times 2 = 4\end{align*}. The number 7 is the square root of 49 because \begin{align*}7 \times 7 = 49\end{align*}.

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

What is the nature of the roots of a 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 are the nature of roots Class 10?

Nature of Roots

(i) two distinct real roots, if b² – 4ac > 0, (ii) two equal real roots, if b² – 4ac = 0, (iii) no real roots, if b² – 4ac < 0.

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.

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 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 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 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 quadratic equation has irrational roots?

ax2 + bx + c = 0 where, the coefficients a, b and c are real. Let p + √q (where p is rational and √q is irrational) be a surd root of equation ax2 + bx + c = 0. Then the equation ax2 + bx + c = 0 must be satisfied by x = p + √q.

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 the roots of the quadratic equation 9x² 12x 4 0 *?

∴ b² – 4ac > 0. hence, roots are real and equal.

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 3x² 4x 2 0?

Answer: The roots of the equation 3x² - 4x - 2 = 0 are real and unequal.

How do you describe the nature of the roots of 3x² 4x 5 0?

Imaginary roots. Also the discriminant is b² - 4ac = -44 < 0. Thus we have imaginary roots. Therefore, the best description of the roots of the equation 3x² - 4x + 5 = 0 is imaginary roots.

What is the sum of roots?

For any quadratic equation ax² + bx + c = 0, the sum of the roots = -b/a. the product of the roots = c/a.

Which of the following is not a quadratic equation?

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

What will be the nature of roots of quadratic equation 2x 2 )+ 4x and 0?

D =0 roots are real and equal.