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?

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

What is the nature of the roots of a quadratic equation if the discriminant is greater than zero but not a perfect square?

When a, b, and c are real numbers, a ≠ 0 and the discriminant is positive but not a perfect square then the roots of the quadratic equation ax² + bx + c = 0 are real, irrational and unequal.

What is the nature of the roots of the quadratic equation if the discriminant is greater than 0?

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 the roots of a quadratic equation with a discriminant of 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 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.

The Nature of the Roots of a Quadratic Equation | Discriminant of Quadratic Equation | Mathusay

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 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 4m2 8m 9 0?

✰ Solution :-

∴ Quadratic equation have non - real roots.

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

Answer: The roots are real and distinct.

What will be the nature of the roots if the discriminant is equal to 49?

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

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 is the nature of the solution of a quadratic equation if the value of the discriminant is positive and a perfect square?

If the discriminant is a perfect square, then the solutions to the equation are not only real, but also rational. If the discriminant is positive but not a perfect square, then the solutions to the equation are real but irrational.

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 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.

What nature of root is 144?

The value of the square root of 144 is equal to 12. In radical form, it is denoted as √144 = 12. To calculate the value to root 144 without using a calculator, there are two methods: one is the prime factorisation and another is the long division method.

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.

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

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

What is the nature of the roots when the discriminant is?

Nature of Roots depending upon Discriminant

If the discriminant is equal to zero (b² – 4ac = 0), a, b, c are real numbers, a≠0, then the roots of the quadratic equation ax² + bx + c = 0, are real and equal. In this case, the roots are x = -b/2a.

What is the nature of discriminant?

Interpret the Discriminant of a Quadratic Equation

The sign of the discriminant tells us the nature of the solutions ( or roots ) of a quadratic equation. We can obtain two distinct real solutions if , two non-real solutions if or one solution ( called a double root ) if .

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.