2x² - 6x + 9/2 = 0. State whether the following quadratic equation has two distinct real roots
Solution:
Given, the equation is 2x² - 6x + 9/2 = 0
We have to determine if the equation has two distinct real roots.
Discriminant = b² - 4ac
Here, a = 2, b = -6 and c = 9/2
b² - 4ac = (-6)² - 4(2)(9/2)
= 36 - 36
= 0
We know that a quadratic equation ax² + bx + c = 0 has equal roots when the discriminant of the equation is zero.
Therefore, the equation has 2 equal roots.
✦ Try This: Determine the nature of the quadratic equation 2x² + x - 3 = 0
Given, the equation is 2x² + x - 3 = 0
We have to determine if the equation has two distinct real roots.
Discriminant = b² - 4ac
Here, a = 2, b = 1 and c = -3
b² - 4ac = (1)² - 4(2)(-3)
= 1 + 24
= 25 > 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 (iii)
2x² - 6x + 9/2 = 0. State whether the following quadratic equation has two distinct real roots
Summary:
The equation 2x² - 6x + 9/2 = 0 does not have 2 distinct real roots, it has 2 equal roots.
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