Which of the following equations has no real roots
a. x² - 4x + 3√2 = 0
b. x² + 4x - 3√2 = 0
c. x² - 4x - 3√2 = 0
d. 3x² + 4√3x + 4 = 0
Solution:
We have to find an equation that has no real roots.
A quadratic equation ax² + bx + c = 0 has no real roots when the discriminant of the equation is less than zero.
Discriminant = b² - 4ac
From the options,
A) x² - 4x + 3√2 = 0
Here, a = 1, b = -4 and c = 3√2
b² - 4ac = (-4)² - 4(1)(3√2)
= 16 - 12√2
= 16 - 12(1.414)
= 16 - 16.968
= -0.968 < 0
Therefore, the equation has no real roots.
B) x² + 4x - 3√2 = 0
Here, a = 1, b = 4 and c = -3√2
b² - 4ac = (4)² - 4(1)(-3√2)
= 16 + 12√2 > 0
Therefore, the equation has 2 distinct real roots.
C) x² - 4x - 3√2 = 0
Here, a = 1, b = -4 and c = -3√2
b² - 4ac = (-4)² - 4(1)(-3√2)
= 16 + 12√2 > 0
Therefore, the equation has 2 distinct real roots.
D) 3x² + 4√3x + 4 = 0
Here, a = 3, b = 4√3 and c = 4
b² - 4ac = (4√3)² - 4(3)(4)
= 48 - 48
= 0
Therefore, the equation has 2 equal roots.
✦ Try This: Which of the following equations has no real roots?
- 5x² - 3x + 1 = 0
- x² + 4x - 3√2 = 0
- x² - 4x - 3√2 = 0
- 3x² + 4√3x + 4 = 0
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 4
NCERT Exemplar Class 10 Maths Exercise 4.1 Problem 10
Which of the following equations has no real roots, a. x² - 4x + 3√2 = 0, b. x² + 4x - 3√2 = 0, c. x² - 4x - 3√2 = 0, d. 3x² + 4√3x + 4 = 0
Summary:
The equation x² - 4x + 3√2 = 0 has no real roots.
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