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Find the values of ‘a’ for which the equation (x^2 x 2)^2 - (a-3)(x^2 x 1)(x^2 x 1) (a-4)(x^2 x 1)^2=0 has at least one real root?
Most Upvoted Answer
Find the values of ‘a’ for which the equation (x^2 x 2)^2 - (a-3)(x^2 ...
To find the values of 'a' for which the equation has at least one real root, let's solve the equation step by step.
Step 1: Expand the equation
(x^2 + 2)^2 - (a-3)(x^2 + 1)(x^2 + 1)(a-4)(x^2 + 1)^2 = 0
Step 2: Simplify the equation
(x^4 + 4x^2 + 4) - (a-3)(x^2 + 1)(x^2 + 1)(a-4)(x^2 + 1)^2 = 0
Step 3: Expand and simplify further
x^4 + 4x^2 + 4 - (a-3)(x^2 + 1)(x^2 + 1)(a-4)(x^2 + 1)^2 = 0
Step 4: Expand and simplify the quadratic terms
x^4 + 4x^2 + 4 - (a-3)(x^2 + 1)(x^2 + 1)(a-4)(x^4 + 2x^2 + 1) = 0
Step 5: Distribute and combine like terms
x^4 + 4x^2 + 4 - (a-3)(a-4)(x^4 + 2x^2 + 1)(x^2 + 1) = 0
Step 6: Expand and simplify further
x^4 + 4x^2 + 4 - (a^2 - 7a + 12)(x^4 + 2x^2 + 1)(x^2 + 1) = 0
Step 7: Distribute and combine like terms
x^4 + 4x^2 + 4 - (a^2 - 7a + 12)(x^6 + 3x^4 + 3x^2 + x^2 + 1) = 0
Step 8: Simplify the equation
x^4 + 4x^2 + 4 - (a^2 - 7a + 12)(x^6 + 4x^4 + 4x^2 + 1) = 0
Step 9: Distribute and combine like terms
x^4 + 4x^2 + 4 - (a^2 - 7a + 12)x^6 - (a^2 - 7a + 12)4x^4 - (a^2 - 7a + 12)4x^2 - (a^2 - 7a + 12) = 0
Step 10: Rearrange the terms
(a^2 - 7a + 12)x^6 + (a^2 - 7a + 12)4x^4 + (a^2 - 7a + 12)4x^2 + x^4 + 4x^2 + 4 - (a^2 - 7a + 12) = 0
Step 11: Combine like terms
(a^2 - 7a + 12)x^6 + (4a^2 - 28a
Step 1: Expand the equation
(x^2 + 2)^2 - (a-3)(x^2 + 1)(x^2 + 1)(a-4)(x^2 + 1)^2 = 0
Step 2: Simplify the equation
(x^4 + 4x^2 + 4) - (a-3)(x^2 + 1)(x^2 + 1)(a-4)(x^2 + 1)^2 = 0
Step 3: Expand and simplify further
x^4 + 4x^2 + 4 - (a-3)(x^2 + 1)(x^2 + 1)(a-4)(x^2 + 1)^2 = 0
Step 4: Expand and simplify the quadratic terms
x^4 + 4x^2 + 4 - (a-3)(x^2 + 1)(x^2 + 1)(a-4)(x^4 + 2x^2 + 1) = 0
Step 5: Distribute and combine like terms
x^4 + 4x^2 + 4 - (a-3)(a-4)(x^4 + 2x^2 + 1)(x^2 + 1) = 0
Step 6: Expand and simplify further
x^4 + 4x^2 + 4 - (a^2 - 7a + 12)(x^4 + 2x^2 + 1)(x^2 + 1) = 0
Step 7: Distribute and combine like terms
x^4 + 4x^2 + 4 - (a^2 - 7a + 12)(x^6 + 3x^4 + 3x^2 + x^2 + 1) = 0
Step 8: Simplify the equation
x^4 + 4x^2 + 4 - (a^2 - 7a + 12)(x^6 + 4x^4 + 4x^2 + 1) = 0
Step 9: Distribute and combine like terms
x^4 + 4x^2 + 4 - (a^2 - 7a + 12)x^6 - (a^2 - 7a + 12)4x^4 - (a^2 - 7a + 12)4x^2 - (a^2 - 7a + 12) = 0
Step 10: Rearrange the terms
(a^2 - 7a + 12)x^6 + (a^2 - 7a + 12)4x^4 + (a^2 - 7a + 12)4x^2 + x^4 + 4x^2 + 4 - (a^2 - 7a + 12) = 0
Step 11: Combine like terms
(a^2 - 7a + 12)x^6 + (4a^2 - 28a
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Find the values of ‘a’ for which the equation (x^2 x 2)^2 - (a-3)(x^2 x 1)(x^2 x 1) (a-4)(x^2 x 1)^2=0 has at least one real root?
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Find the values of ‘a’ for which the equation (x^2 x 2)^2 - (a-3)(x^2 x 1)(x^2 x 1) (a-4)(x^2 x 1)^2=0 has at least one real root? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Find the values of ‘a’ for which the equation (x^2 x 2)^2 - (a-3)(x^2 x 1)(x^2 x 1) (a-4)(x^2 x 1)^2=0 has at least one real root? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the values of ‘a’ for which the equation (x^2 x 2)^2 - (a-3)(x^2 x 1)(x^2 x 1) (a-4)(x^2 x 1)^2=0 has at least one real root?.
Find the values of ‘a’ for which the equation (x^2 x 2)^2 - (a-3)(x^2 x 1)(x^2 x 1) (a-4)(x^2 x 1)^2=0 has at least one real root? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Find the values of ‘a’ for which the equation (x^2 x 2)^2 - (a-3)(x^2 x 1)(x^2 x 1) (a-4)(x^2 x 1)^2=0 has at least one real root? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the values of ‘a’ for which the equation (x^2 x 2)^2 - (a-3)(x^2 x 1)(x^2 x 1) (a-4)(x^2 x 1)^2=0 has at least one real root?.
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