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If alpha(@) and beta($) are zeros of polynomial ax²+ bx+ c then find the value of
1). 1/@-1/$
2) 1/@² +1/$²
3). 1/@²+ 1/$²-2@$
here (@)means alpha and ($)means beta.?
1). 1/@-1/$
2) 1/@² +1/$²
3). 1/@²+ 1/$²-2@$
here (@)means alpha and ($)means beta.?
Most Upvoted Answer
If alpha(@) and beta($) are zeros of polynomial ax²+ bx+ c then find t...
Solution:
Given, alpha(@) and beta($) are zeros of polynomial ax² + bx + c.
We know that the sum of the roots of a quadratic equation is -b/a and the product of the roots is c/a.
Therefore, in this case, we have @ + $ = -b/a and @ $ = c/a.
1) To find the value of 1/@ - 1/$, we can write it as [(1/@)($/$) - (1/$)($/$)]/($/$) = ($ - @)/($ @). Substituting the values of @ and $ from above, we get ($ - @)/c/a = ($ - @)/(ab/c) = -b/c.
Therefore, the value of 1/@ - 1/$ is -b/c.
2) To find the value of 1/@² + 1/$², we can write it as [(1/@)²($/$)² + (1/$)²($/$)²]/($/$)² = (@² + $²)/c²/a². Substituting the values of @ and $ from above, we get (@² + $²)/(ab)²/c² = [(b² - 2ac) + 2ac]/(a²b²c²) = (b² + 2ac)/(a²b²c²).
Therefore, the value of 1/@² + 1/$² is (b² + 2ac)/(a²b²c²).
3) To find the value of 1/@² + 1/$² - 2@$, we can substitute the values of @ and $ from above and simplify to get [(b² + 2ac)/(a²b²c²)] - 2@$/a. Multiplying both numerator and denominator of the first term by a, we get [(ab)² + 2abc]/(a³b³c²) - 2@$/a = [b² + 2ac - 2@$/b]/(a²b²c²).
Therefore, the value of 1/@² + 1/$² - 2@$ is [b² + 2ac - 2@$/b]/(a²b²c²).
Given, alpha(@) and beta($) are zeros of polynomial ax² + bx + c.
We know that the sum of the roots of a quadratic equation is -b/a and the product of the roots is c/a.
Therefore, in this case, we have @ + $ = -b/a and @ $ = c/a.
1) To find the value of 1/@ - 1/$, we can write it as [(1/@)($/$) - (1/$)($/$)]/($/$) = ($ - @)/($ @). Substituting the values of @ and $ from above, we get ($ - @)/c/a = ($ - @)/(ab/c) = -b/c.
Therefore, the value of 1/@ - 1/$ is -b/c.
2) To find the value of 1/@² + 1/$², we can write it as [(1/@)²($/$)² + (1/$)²($/$)²]/($/$)² = (@² + $²)/c²/a². Substituting the values of @ and $ from above, we get (@² + $²)/(ab)²/c² = [(b² - 2ac) + 2ac]/(a²b²c²) = (b² + 2ac)/(a²b²c²).
Therefore, the value of 1/@² + 1/$² is (b² + 2ac)/(a²b²c²).
3) To find the value of 1/@² + 1/$² - 2@$, we can substitute the values of @ and $ from above and simplify to get [(b² + 2ac)/(a²b²c²)] - 2@$/a. Multiplying both numerator and denominator of the first term by a, we get [(ab)² + 2abc]/(a³b³c²) - 2@$/a = [b² + 2ac - 2@$/b]/(a²b²c²).
Therefore, the value of 1/@² + 1/$² - 2@$ is [b² + 2ac - 2@$/b]/(a²b²c²).
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If alpha(@) and beta($) are zeros of polynomial ax²+ bx+ c then find t...
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If alpha(@) and beta($) are zeros of polynomial ax²+ bx+ c then find the value of 1). 1/@-1/$ 2) 1/@² +1/$² 3). 1/@²+ 1/$²-2@$ here (@)means alpha and ($)means beta.?
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If alpha(@) and beta($) are zeros of polynomial ax²+ bx+ c then find the value of 1). 1/@-1/$ 2) 1/@² +1/$² 3). 1/@²+ 1/$²-2@$ here (@)means alpha and ($)means beta.? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If alpha(@) and beta($) are zeros of polynomial ax²+ bx+ c then find the value of 1). 1/@-1/$ 2) 1/@² +1/$² 3). 1/@²+ 1/$²-2@$ here (@)means alpha and ($)means beta.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If alpha(@) and beta($) are zeros of polynomial ax²+ bx+ c then find the value of 1). 1/@-1/$ 2) 1/@² +1/$² 3). 1/@²+ 1/$²-2@$ here (@)means alpha and ($)means beta.?.
If alpha(@) and beta($) are zeros of polynomial ax²+ bx+ c then find the value of 1). 1/@-1/$ 2) 1/@² +1/$² 3). 1/@²+ 1/$²-2@$ here (@)means alpha and ($)means beta.? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If alpha(@) and beta($) are zeros of polynomial ax²+ bx+ c then find the value of 1). 1/@-1/$ 2) 1/@² +1/$² 3). 1/@²+ 1/$²-2@$ here (@)means alpha and ($)means beta.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If alpha(@) and beta($) are zeros of polynomial ax²+ bx+ c then find the value of 1). 1/@-1/$ 2) 1/@² +1/$² 3). 1/@²+ 1/$²-2@$ here (@)means alpha and ($)means beta.?.
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