3x² - 4x + 1 = 0. State whether the following quadratic equation has two distinct real roots
Solution:
Given, the equation is 3x² - 4x + 1 = 0
We have to determine if the equation has two distinct real roots.
Discriminant = b² - 4ac
Here, a = 3, b = -4 and c = 1
b² - 4ac = (-4)² - 4(3)(1)
= 16 - 12
= 4 > 0
We know that a quadratic equation ax² + bx + c = 0 has 2 distinct real roots when the discriminant of the equation is greater than zero.
Therefore, the equation has 2 distinct real roots.
✦ Try This: Determine the nature of the quadratic equation x² + x - 3 = 0.
Given, the equation is x² + x - 3 = 0
We have to determine if the equation has two distinct real roots.
Discriminant = b² - 4ac
Here, a = 1, b = 1 and c = -3
b² - 4ac = (1)² - 4(1)(-3)
= 1 + 12
= 13 > 0
We know that a quadratic equation ax² + bx + c = 0 has 2 distinct real roots when the discriminant of the equation is greater than zero.
Therefore, the equation has 2 distinct real roots.
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 4
NCERT Exemplar Class 10 Maths Exercise 4.2 Problem 1 (iv)
3x² - 4x + 1 = 0. State whether the following quadratic equation has two distinct real roots
Summary:
The equation 3x² - 4x + 1 = 0 has 2 distinct real roots
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