Which of the following equations has two distinct real roots
a. 2x² - 3√2x + 9/4 = 0
b. x² + x - 5 = 0
c. x² + 3x + 2√2 = 0
d. 5x² - 3x + 1 = 0
Solution:
We have to find the equation which has two distinct real roots.
A quadratic equation ax² + bx + c = 0 has 2 distinct real roots when the discriminant of the equation is greater than zero.
Discriminant = b² - 4ac
From the options,
A) 2x² - 3√2x + 9/4 = 0
Here, a = 2, b = -3√2 and c = 9/4
b² - 4ac = (-3√2)² - 4(2)(9/4)
= 18 - 18
= 0
Therefore, the equation has equal roots.
B) x² + x - 5 = 0
Here, a = 1, b = 1 and c = -5
b² - 4ac = (1)² - 4(1)(-5)
= 1 + 20
= 21 > 0
Therefore, the equation has 2 distinct real roots.
C) x² + 3x + 2√2 = 0
Here, a = 1, b = 3 and c = 2√2
b² - 4ac = (3)² - 4(1)(2√2)
= 9 - 8√2 < 0
Therefore, the equation has no real roots.
D) 5x² - 3x + 1 = 0
Here, a = 5, b = -3 and c = 1
b² - 4ac = (-3)² - 4(5)(1)
= 9 - 20
= -11 < 0
Therefore, the equation has no real roots.
✦ Try This: Which of the following equations has two distinct real roots?
- 2x² - 3√2x + 9/4 = 0
- x² + 4x - 3√2 = 0
- x² + 3x + 2√2 = 0
- 5x² - 3x + 1 = 0
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 4
NCERT Exemplar Class 10 Maths Exercise 4.1 Problem 9
Which of the following equations has two distinct real roots, a. 2x² - 3√2x + 9/4 = 0, b. x² + x - 5 = 0, c. x² + 3x + 2√2 = 0, d. 5x² - 3x + 1 = 0
Summary:
The equation x² + x - 5 = 0 has 2 distinct real roots
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