Every quadratic equation has at most two roots, write whether the following statement is true or false
Solution:
We have to determine if every quadratic equation has at most two roots.
Quadratic equations are second-degree algebraic expressions.
In other words, 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.
So, it is clear that all quadratic equations have 2 roots.
Therefore, it is true.
✦ Try This: Determine the roots of the equation 3x² - 4x + 1 = 0.
Given, the equation is 3x² - 4x + 1 = 0
We have to determine if the equation has two distinct real roots.
Discriminant = b² - 4ac
Here, a = 3, b = -4 and c = 1
b² - 4ac = (-4)² - 4(3)(1)
= 16 - 12
= 4 > 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 2 (iv)
Every quadratic equation has at most two roots, write whether the following statement is true or false
Summary:
The assumption “every quadratic equation has at most two roots” is a true statement.
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