Question

what can you say about the zero of the polynomial x^2-77x+360?​

Answer 1

Given polynomial :

x² - 77x + 360

To find :

Nature of roots

Solution :

To find the nature of roots, we have to find the value of discriminant, nature of roots can be determined easily by having the value of discriminant.

To find the discriminant, we have formula :-

⟹ D = b² - 4ac

Here :-

• D = discriminant
• b = coefficient of x
• a = coefficient of x²
• c = constant term

⟹ D = (-77)² - 4 (1) (360)

⟹ D = 5929 - 1440

⟹ D = 4489

Here the value of discriminant is positive, it means that the given polynomial has two distinct roots.

∴ We can say that the given polynomial has two distinct roots.

More :-

• If the value of discriminant is 0, it means that the polynomial has two equal roots.

• If the value of discriminant is negative, this implies that the polynomial has no real roots or has imaginary roots.