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If alpha and beta are zeros of quadratic polynomial f (x) = x squared- p X + Q then find the value of Alpha square + beta square and one upon alpha plus one upon beta?????somebody know the answer....
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If alpha and beta are zeros of quadratic polynomial f (x) = x squared...
Solution:
Given, the quadratic polynomial is f(x) = x^2 - p x q.
Let α and β be the roots of the given quadratic polynomial.
Product of roots formula:
The product of roots of the quadratic equation ax^2 + bx + c = 0 is given by
α.β = c/a
So, αβ = q/p
Sum of roots formula:
The sum of roots of the quadratic equation ax^2 + bx + c = 0 is given by
α + β = -b/a
So, α + β = p
Value of α^2 + β^2:
α^2 + β^2 = (α + β)^2 - 2αβ
= p^2 - 2q/p
Value of 1/α + 1/β:
1/α + 1/β = (α + β)/αβ
= p/q
Therefore, the value of α^2 + β^2 is p^2 - 2q/p and the value of 1/α + 1/β is p/q.
Given, the quadratic polynomial is f(x) = x^2 - p x q.
Let α and β be the roots of the given quadratic polynomial.
Product of roots formula:
The product of roots of the quadratic equation ax^2 + bx + c = 0 is given by
α.β = c/a
So, αβ = q/p
Sum of roots formula:
The sum of roots of the quadratic equation ax^2 + bx + c = 0 is given by
α + β = -b/a
So, α + β = p
Value of α^2 + β^2:
α^2 + β^2 = (α + β)^2 - 2αβ
= p^2 - 2q/p
Value of 1/α + 1/β:
1/α + 1/β = (α + β)/αβ
= p/q
Therefore, the value of α^2 + β^2 is p^2 - 2q/p and the value of 1/α + 1/β is p/q.
Community Answer
If alpha and beta are zeros of quadratic polynomial f (x) = x squared...
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If alpha and beta are zeros of quadratic polynomial f (x) = x squared- p X + Q then find the value of Alpha square + beta square and one upon alpha plus one upon beta?????somebody know the answer....
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