2x² + x - 1 = 0. State whether the following quadratic equation has two distinct real roots
Solution:
Given, the equation is 2x² + x - 1 = 0
We have to determine if the equation has two distinct real roots.
Discriminant = b² - 4ac
Here, a = 2, b = 1 and c = -1
b² - 4ac = (1)² - 4(2)(-1)
= 1 + 8
= 9 > 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 - 1 = 0.
Given, the equation is x² + x - 1 = 0
We have to determine if the equation has two distinct real roots.
Discriminant = b² - 4ac
Here, a = 1, b = 1 and c = -1
b² - 4ac = 1 - 4(1)(-1)
= 1 + 4
= 5 > 0
Therefore, the equation has 2 distinct and real root
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 4
NCERT Exemplar Class 10 Maths Exercise 4.2 Problem 1 (ii)
2x² + x - 1 = 0. State whether the following quadratic equation has two distinct real roots
Summary:
The quadratic equation 2x² + x - 1 = 0 has 2 distinct real roots
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