Question

If Alpha, Beta Are Zeroes of x^2+5x+5, Find A Polynomial With Zeroes 1/Alpha And 1/Beta

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Answer 1

Step-by-step explanation:

Given:-

x^2+5x+5

To find:-

If α and β are the zeroes of x^2+5x+5 then Find a Polynomial with zeroes 1/α and 1/β?

Solution :-

Given quardratic polynomial is x^2+5x+5

On Comparing this with the standard quadratic Polynomial ax^2+bx+c

a = 1

b= 5

c= 5

We know that

Sum of the zeroes = -b/a

=> α + β = -5/1

α + β = -5 -------(1)

Product of the zeroes = c/a

α β = 5/1

α β = 5---------(2)

We know that

The Quadratic Polynomial whose zeroes (1/α) and (1/β) is K[x^2-[(1/α)+(1/β)]x+(1/α)(1/β)]

=> K[x^2-{(α + β)/α β}x +(1/α β)]

=>K[x^2-(-5/5)x+(1/5)]

=>K[x^2-(-1)x+(1/5)]

=>K[x^2+x+(1/5)]

=> K[5x^2+5x+1]/5

If K = 5 then

=> 5[5x^2+5x+1]/5

=>5^2+5x+1

Answer:-

The required quardratic polynomial is 5^2+5x+1

Used formulae:-

• The standard quadratic Polynomial ax^2+bx+c

• Sum of the zeroes = -b/a

• Product of the zeroes = c/a

• The Quadratic Polynomial whose zeroes α and β is K[x^2-(α+β)x+αβ]