(x + 1)(x - 2) + x = 0. State whether the following quadratic equation has two distinct real roots
Solution:
Given, the equation is (x + 1)(x - 2) + x = 0
We have to determine if the equation has two distinct real roots.
By multiplicative and distributive property,
(x + 1)(x - 2) + x = 0
x² - 2x + x - 2 + x = 0
x² - x - 2 + x = 0
x² - 2 = 0
Discriminant = b² - 4ac
Here, a = 1, b = 0 and c = -2
b² - 4ac = (0)² - 4(1)(-2)
= 8 > 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 7x² + 2x - 1 = 0
Given, the equation is x² + x - 3 = 0
We have to determine if the equation has two distinct real roots.
Discriminant = b² - 4ac
Here, a = 7, b = 2 and c = -1
b² - 4ac = (2)² - 4(7)(-1)
= 4 + 28
= 32 > 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 (x)
(x + 1)(x - 2) + x = 0. State whether the following quadratic equation has two distinct real roots
Summary:
The equation (x + 1)(x - 2) + x = 0 has 2 distinct real roots since the discriminant of the equation is greater than zero.
☛ Related Questions:
- Every quadratic equation has exactly one root, write whether the following statement is true or fals . . . .
- Every quadratic equation has at least one real root, write whether the following statement is true o . . . .
- Every quadratic equation has at least two roots, write whether the following statement is true or fa . . . .
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