Read the following statements carefully: Statement I: Every quadratic equation has exactly one root. Statement II: Every quadratic equations has at most two roots.
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Answer:
Statement 2 is correct as it is not true that everyone time quadratic equation has 1 root
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Statement I: Every quadratic equation has exactly one root is FALSE
Statement II: Every quadratic equations has at most two roots is TRUE
Given:
- Two Statements
- Statement I: Every quadratic equation has exactly one root.
- Statement II: Every quadratic equations has at most two roots.
To Find:
- True or False
Solution:
- Quadratic equation is of the form ax²+bx+c=0 where a , b and c are real also a≠0.
- D = b²-4ac is called discriminant.
- D >0 roots are real and distinct
- D =0 roots are real and equal (Hence one root)
- D < 0 roots are imaginary ( not real ) and different ( hence no roots)
Statement I: Every quadratic equation has exactly one root
This is False
For example : x² - 1 = 0 has two roots -1 and 1
x² -2x + 1 = 0 has 1 root 1
x² + 2 = 0 has no real roots
Statement II: Every quadratic equations has at most two roots.
This is True
Roots can not be more than degree of Equation.
Degree of Quadratic Equation is 2, hence maximum roots are 2.
Statement I: Every quadratic equation has exactly one root is FALSE
Statement II: Every quadratic equations has at most two roots is TRUE
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