Does (x - 1)² + 2(x + 1) = 0 have a real root
Solution:
Given, the equation is (x - 1)² + 2(x + 1) = 0
We have to determine if the equation has a real root.
By using algebraic identity,
(a - b)² = a² - 2ab + b²
(x - 1)² = x² - 2x + 1
By multiplicative and distributive property,
2(x + 1) = 2x + 2
Now, x² - 2x + 1 +2x + 2 = 0
By grouping,
x² - 2x + 2x + 1 + 3 = 0
x² + 3 = 0
Here, a = 1, b = 0 and c = 3
b² - 4ac = 0 - 4(1)(3)
= -12 < 0
A quadratic equation ax² + bx + c = 0 has no real roots when the discriminant of the equation is less than zero.
Therefore, the equation has no real roots.
✦ Try This: Does (x - 1)² + 2(x + 1) = 0 have a real root? Justify your answer
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 4
NCERT Exemplar Class 10 Maths Exercise 4.2 Sample Problem 1
Does (x - 1)² + 2(x + 1) = 0 have a real root
Summary:
The equation (x - 1)² + 2(x + 1) = 0 has no real roots
☛ Related Questions:
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