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

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

We have calculated that Δ>0 and is not a perfect square, therefore we can conclude that the roots are real, unequal and irrational.

What is the nature of the roots with value of the discriminant greater than 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.

What if the discriminant is greater than zero and a perfect square?

The discriminant is 0, so the equation has a double root. 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 is the nature of the roots of the quadratic equation if the value of its discriminant is 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.

How To Determine The Discriminant of a Quadratic Equation

What is the nature of 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.

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 does it mean if 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. In this case, we have two real roots.

How does the discriminant determine the nature of the roots?

Determining the Nature of Roots

The discriminant is negative, so the equation has two non-real solutions. The discriminant is 0, so the equation has a double root. If the discriminant is a perfect square, then the solutions to the equation are not only real, but also rational.

What is the nature of solution if D 0?

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

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 happens when the discriminant is less than 0?

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.

How many solutions does the discriminant have greater than zero?

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 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 4x2 8x 9 0?

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

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 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 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 nature of roots of 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.

When the discriminant is zero how many real solutions does the quadratic equation have?

If the discriminant is equal to 0, the quadratic equation has 1 real solution. If the discriminant is less than 0, the quadratic equation has 0 real solutions.

What will be the nature of roots if discriminant of any quadratic equation is less than zero?

If the discriminant is less than zero, the equation will have no real roots, it will have 2 complex roots.

What if the discriminant is negative?

A negative discriminant indicates that neither of the solutions are real numbers.