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If alpha and beta r two zeros of the quadratic polynomial f (x)=x^2 x-2 so find the value of 1/alpha -1/ beta?
Most Upvoted Answer
If alpha and beta r two zeros of the quadratic polynomial f (x)=x^2 x-...
Solution:
Given quadratic polynomial is f(x) = x^2 - 2
Let α and β be the zeros of the polynomial f(x).
We know that the sum of the roots of a quadratic equation is equal to -b/a
Here, sum of the roots α and β = α + β = 0 (since there is no x term in the polynomial)
Therefore, α = -β
We need to find the value of 1/α - 1/β
= (β - α)/αβ (taking LCM)
= (β - (-β))/αβ (since α = -β)
= 2β/αβ
= 2/α (since α = -β)
= -2/β (since α = -β)
Therefore, the value of 1/α - 1/β is -2/β.
Hence, the answer is -2/β.
Given quadratic polynomial is f(x) = x^2 - 2
Let α and β be the zeros of the polynomial f(x).
We know that the sum of the roots of a quadratic equation is equal to -b/a
Here, sum of the roots α and β = α + β = 0 (since there is no x term in the polynomial)
Therefore, α = -β
We need to find the value of 1/α - 1/β
= (β - α)/αβ (taking LCM)
= (β - (-β))/αβ (since α = -β)
= 2β/αβ
= 2/α (since α = -β)
= -2/β (since α = -β)
Therefore, the value of 1/α - 1/β is -2/β.
Hence, the answer is -2/β.
Community Answer
If alpha and beta r two zeros of the quadratic polynomial f (x)=x^2 x-...
• One way is to find the roots itself:
x² + x - 2 = 0
x² + 2x - x - 2 = 0
x(x + 2) - 1(x + 2) = 0
(x + 2)(x - 1) = 0
x = 1,-2
1/a - 1/b = ± 3/2 (depending on what values are taken for a and b)
• Another way:
a + b = -1 and ab = -2
a - b = √{(a + b)² - 4ab} = √(1 + 8)
= ± 3
1/a - 1/b = (a - b)/ab
= ± 3/2
x² + x - 2 = 0
x² + 2x - x - 2 = 0
x(x + 2) - 1(x + 2) = 0
(x + 2)(x - 1) = 0
x = 1,-2
1/a - 1/b = ± 3/2 (depending on what values are taken for a and b)
• Another way:
a + b = -1 and ab = -2
a - b = √{(a + b)² - 4ab} = √(1 + 8)
= ± 3
1/a - 1/b = (a - b)/ab
= ± 3/2
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If alpha and beta r two zeros of the quadratic polynomial f (x)=x^2 x-2 so find the value of 1/alpha -1/ beta?
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If alpha and beta r two zeros of the quadratic polynomial f (x)=x^2 x-2 so find the value of 1/alpha -1/ 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 r two zeros of the quadratic polynomial f (x)=x^2 x-2 so find the value of 1/alpha -1/ 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 r two zeros of the quadratic polynomial f (x)=x^2 x-2 so find the value of 1/alpha -1/ beta?.
If alpha and beta r two zeros of the quadratic polynomial f (x)=x^2 x-2 so find the value of 1/alpha -1/ 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 r two zeros of the quadratic polynomial f (x)=x^2 x-2 so find the value of 1/alpha -1/ 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 r two zeros of the quadratic polynomial f (x)=x^2 x-2 so find the value of 1/alpha -1/ beta?.
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