A quadratic equation with integral coefficient has integral roots
Solution:
Given, the quadratic equation has integral coefficients.
We have to determine if the equation has integral 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 roots can be integral or non-integral.
✦ Try This: Determine the roots of the equation 6x² - 2x - 1 = 0.
Given the equation is 6x² - x - 1 = 0.
We have to determine the roots of the equation.
Using the quadratic formula,
x = [-b ± √b² - 4ac]/2a
Here, a = 6, b = -1 and c = -1
x = [-(-1) ± √(-1)² - 4(6)(-1)]/2(6)
x = [1 ± √1 + 24]/ 12
x = [1 ± √25]/12
x = [1 ± 5]/12
Now, x = (1 + 5)/12 = 6/12 = 1/2
x = (1 - 5)/12 = -4/12 = -1/3
Therefore, the roots of the equation are 1/2 and -1/3 which are not integral roots
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 4
NCERT Exemplar Class 10 Maths Exercise 4.2 Problem 3
A quadratic equation with integral coefficient has integral roots
Summary:
The statement “a quadratic equation with integral coefficient has integral roots” is false.
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