Class 10 Exam > Class 10 Questions > (x2 + 1)2 - x2 = 0 hasa)Four real rootsb)Two ...
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(x2 + 1)2 - x2 = 0 has
- a)Four real roots
- b)Two real roots
- c)No real roots
- d)One real root
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
(x2 + 1)2 - x2 = 0 hasa)Four real rootsb)Two real rootsc)No real roots...
Given equation is (x2 + 1)2 - x2 = 0
⇒ x4 + 1 + 2x2 - x2 = 0 [∵ (a + b)2 = a2 + b2 + 2ab]
⇒ x4 + x2 + 1 = 0
Let x2 = y
∴ (x2)2 + x2 + 1 = 0
y2 + y + 1 = 0
On comparing with ay2 + by + c = 0, we get
a = 1, b = 1 and c = 1
Discriminant, D = b2 - 4ac
= (1)2 - 4(1)(1)
= 1 - 4 = -3
Since, D < 0
∴ y2 + y + 1 = 0 i.e., x4 + x2 + 1 = 0 or (x2 + 1)2 - x2 = 0 has no real roots.
⇒ x4 + 1 + 2x2 - x2 = 0 [∵ (a + b)2 = a2 + b2 + 2ab]
⇒ x4 + x2 + 1 = 0
Let x2 = y
∴ (x2)2 + x2 + 1 = 0
y2 + y + 1 = 0
On comparing with ay2 + by + c = 0, we get
a = 1, b = 1 and c = 1
Discriminant, D = b2 - 4ac
= (1)2 - 4(1)(1)
= 1 - 4 = -3
Since, D < 0
∴ y2 + y + 1 = 0 i.e., x4 + x2 + 1 = 0 or (x2 + 1)2 - x2 = 0 has no real roots.
Most Upvoted Answer
(x2 + 1)2 - x2 = 0 hasa)Four real rootsb)Two real rootsc)No real roots...
Given equation is (x2 + 1)2 - x2 = 0
⇒ x4 + 1 + 2x2 - x2 = 0 [∵ (a + b)2 = a2 + b2 + 2ab]
⇒ x4 + x2 + 1 = 0
Let x2 = y
∴ (x2)2 + x2 + 1 = 0
y2 + y + 1 = 0
On comparing with ay2 + by + c = 0, we get
a = 1, b = 1 and c = 1
Discriminant, D = b2 - 4ac
= (1)2 - 4(1)(1)
= 1 - 4 = -3
Since, D < 0
∴ y2 + y + 1 = 0 i.e., x4 + x2 + 1 = 0 or (x2 + 1)2 - x2 = 0 has no real roots.
⇒ x4 + 1 + 2x2 - x2 = 0 [∵ (a + b)2 = a2 + b2 + 2ab]
⇒ x4 + x2 + 1 = 0
Let x2 = y
∴ (x2)2 + x2 + 1 = 0
y2 + y + 1 = 0
On comparing with ay2 + by + c = 0, we get
a = 1, b = 1 and c = 1
Discriminant, D = b2 - 4ac
= (1)2 - 4(1)(1)
= 1 - 4 = -3
Since, D < 0
∴ y2 + y + 1 = 0 i.e., x4 + x2 + 1 = 0 or (x2 + 1)2 - x2 = 0 has no real roots.
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(x2 + 1)2 - x2 = 0 hasa)Four real rootsb)Two real rootsc)No real rootsd)One real rootCorrect answer is option 'C'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about (x2 + 1)2 - x2 = 0 hasa)Four real rootsb)Two real rootsc)No real rootsd)One real rootCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for (x2 + 1)2 - x2 = 0 hasa)Four real rootsb)Two real rootsc)No real rootsd)One real rootCorrect answer is option 'C'. Can you explain this answer?.
(x2 + 1)2 - x2 = 0 hasa)Four real rootsb)Two real rootsc)No real rootsd)One real rootCorrect answer is option 'C'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about (x2 + 1)2 - x2 = 0 hasa)Four real rootsb)Two real rootsc)No real rootsd)One real rootCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for (x2 + 1)2 - x2 = 0 hasa)Four real rootsb)Two real rootsc)No real rootsd)One real rootCorrect answer is option 'C'. Can you explain this answer?.
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