Find the Nature of Roots of the given equation (use discriminant)
1.x² + 4x + 4 = 0
2.x² + 7x + 10 = 0
3.x² + 6x + 3 = 0
4.x² - 2x + 5 = 0
Share
Find the Nature of Roots of the given equation (use discriminant)
1.x² + 4x + 4 = 0
2.x² + 7x + 10 = 0
3.x² + 6x + 3 = 0
4.x² - 2x + 5 = 0
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Answer:
To find the nature of roots of a quadratic equation using the discriminant, we need to calculate the discriminant of the equation. The discriminant is given by the formula:
Discriminant (D) = b² - 4ac
Here's the calculation for each given equation:
1. x² + 4x + 4 = 0
a = 1, b = 4, c = 4
D = (4)² - 4(1)(4)
= 16 - 16
= 0
Since the discriminant (D) is zero, the equation has two real and equal roots.
2. x² + 7x + 10 = 0
a = 1, b = 7, c = 10
D = (7)² - 4(1)(10)
= 49 - 40
= 9
Since the discriminant (D) is positive (D > 0), the equation has two distinct real roots.
3. x² + 6x + 3 = 0
a = 1, b = 6, c = 3
D = (6)² - 4(1)(3)
= 36 - 12
= 24
Since the discriminant (D) is positive (D > 0), the equation has two distinct real roots.
4. x² - 2x + 5 = 0
a = 1, b = -2, c = 5
D = (-2)² - 4(1)(5)
= 4 - 20
= -16
Since the discriminant (D) is negative (D < 0), the equation has two complex roots (non-real roots).
Therefore, the nature of the roots for each equation is:
1. Two real and equal roots.
2. Two distinct real roots.
3. Two distinct real roots.
4. Two complex (non-real) roots.