x(1 - x) - 2 = 0. State whether the following quadratic equation has two distinct real roots
Solution:
Given, the equation is x(1 - x) - 2 = 0
We have to determine if the equation has two distinct real roots.
The equation can be written as x - x² - 2 = 0
-x² + x - 2 = 0
x² - x + 2 = 0
Discriminant = b² - 4ac
Here, a = 1, b = -1 and c = 2
b² - 4ac = (-1)² - 4(1)(2)
= 1 - 8
= -7 < 0
We know that a quadratic equation ax² + bx + c = 0 has no real roots when the discriminant of the equation is less than zero.
Therefore, the equation has no real roots.
✦ Try This: Determine the nature of the quadratic equation 5x² + 2x - 3 = 0.
Given, the equation is 5x² + 2x - 3 = 0
We have to determine if the equation has two distinct real roots.
Discriminant = b² - 4ac
Here, a = 5, b = 2 and c = -3
b² - 4ac = (2)² - 4(5)(-3)
= 4 + 60
= 64 > 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 (viii)
x(1 - x) - 2 = 0. State whether the following quadratic equation has two distinct real roots
Summary:
The equation x(1 - x) - 2 = 0 does not have 2 distinct real roots, it has no real roots
☛ Related Questions:
- (x - 1)(x + 2) + 2 = 0. State whether the following quadratic equation has two distinct real roots
- (x + 1)(x - 2) + x = 0. State whether the following quadratic equation has two distinct real roots
- Every quadratic equation has exactly one root, write whether the following statement is true or fals . . . .
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