Every quadratic equation has at least two roots, write whether the following statement is true or false
Solution:
We have to determine if every quadratic equation has at least two roots.
A quadratic equation is an “equation of degree 2” that has two answers for x called the roots of the quadratic equations and are designated as (α, β).
The standard form of a quadratic equation is ax2 + bx + c = 0 in variable x.
Where a, b, and c are real numbers and a ≠ 0.
For example let us consider the quadratic equation x2 - 2x + 1 = 0
Using the quadratic formula,
x = [-b ± √b² - 4ac]/2a
x = [- (-2) ± √(-2)² - 4(1)(1)]/2(1)
x = [2 ± √4 - 4]/2
x = 2/2
x = 1
Therefore, it is false.
✦ Try This: Determine the roots of the quadratic equation x² - 4x + 4 = 0.
Given, the equation is x² - 4x + 4 = 0
We have to find the roots of the equation.
Using the quadratic formula,
x = [-b ± √b² - 4ac]/2a
x = [-(-4) ± √(-4)² - 4(1) (4)]/2(1)
x = [4 ± √16 - 16]/2
x = 4/2
So, x = 2
Therefore, the only root of the equation is 2
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 4
NCERT Exemplar Class 10 Maths Exercise 4.2 Problem 2 (iii)
Every quadratic equation has at least two roots, write whether the following statement is true or false
Summary:
The assumption “every quadratic equation has at least two roots” is false
☛ Related Questions:
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