What is the nature of the solution of a quadratic equation if the value of the discriminant is positive and not a perfect square?

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 roots if the discriminant is positive in 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.

What is the nature of the solution 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 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.

Quadratic Formula - Discriminant is a non-perfect square

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 a quadratic equation with a discriminant of 144?

Because the discriminant is 144>0, there are two real roots.

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 nature of the quadratic equation if the discriminant is less than zero?

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

When the discriminant is negative then the nature of the roots are?

If the discriminant b2−4ac of a quadratic equation is negative, then its roots are imaginary.

What if a quadratic equation is a perfect square?

When a polynomial is multiplied by itself, then it is a perfect square. Example – polynomial ax² + bx + c is a perfect square if b² = 4ac.

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.

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 of the quadratic equation when B 2 4ac is negative?

If D < 0, i.e., b2 – 4ac < 0; i.e., b² – 4ac is negative; the roots are not real, i.e., the roots are imaginary.

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 value of D if the roots of equation ax2 bx c 0 a ≠ 0 are not real?

Hence, for having real and unequal roots the value of D should be >0.

What is the nature of the roots of the quadratic equation 5x2 2x 3 0?

So, the root are imaginary , i.e. it has two non real roots.

What is the nature of the roots of equation 2x2 3x 10 0?

There are no real roots.

What is the nature of the roots of the quadratic equation 2x2 6x 3 0?

As b² – 4ac > 0, Hence, there are distinct real roots exist for this equation, 2x² – 6x + 3 = 0.