Every quadratic equation has at least one real root, write whether the following statement is true or false
Solution:
We have to determine if every quadratic equation has at least one real root.
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.
The roots of the quadratic equation are defined by the formula,
x = [-b ± √b² - 4ac]/2a
For example x² + 1 = 0
x² = - 1
x = √-1
x = i
Therefore, it is false.
✦ Try This: Determine the roots of the quadratic equation x² + 9 = 0
Given, the quadratic equation is x² +9 = 0
We have to determine the roots of the equation.
x² = -9
Since the square root of a negative number is not defined
Therefore, the equation has no real roots
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 4
NCERT Exemplar Class 10 Maths Exercise 4.2 Problem 2 (ii)
Every quadratic equation has at least one real root, write whether the following statement is true or false
Summary:
The assumption “every quadratic equation has at least one real root” is a false statement.
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