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 is the nature of the roots of the quadratic equation if the value of it's discriminant is greater than zero and 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 are the roots if the discriminant is negative?

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

What is the nature of roots of the quadratic equation if the value of the discriminant is zero *?

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 roots of quadratic equation if the value of its discriminant is equal to negative 16?

If the discriminant of the quadratic equation is negative, then the square root of the discriminant will be undefined.

How To Determine The Discriminant of a Quadratic Equation

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 discriminant is?

The discriminant is defined as Δ=b2−4ac. 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.

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 3x 2 4x 2 0?

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

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 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 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.

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 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 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 is the nature of the roots if the discriminant is 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 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.

How do you find the nature of the 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 are 4 examples of quadratic equation?

What are roots of quadratic equation?

Roots of Quadratic Equation. The values of variables satisfying the given quadratic equation are called its roots. In other words, x = α is a root of the quadratic equation f(x), if f(α) = 0. The real roots of an equation f(x) = 0 are the x-coordinates of the points where the curve y = f(x) intersect the x-axis.