Form the quadratic polynomial whose zeroes are - 3 -5- 3 - -5-

The quadratic polynomial whose zeroesare α,β is #160; f(x)=k[x^2 (α+β)x+α.β] Where k is any non zero real number.The quadratic polynomial whose zero ...

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Standard X

Mathematics

Solving a Quadratic Equation by Factorization Method

Form the quad...

Question

Form the quadratic polynomial whose zeroes are : $3 - \sqrt{5}, 3 + \sqrt{5}$ .

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Solution

The quadratic polynomial whose zeroes
are $α, β$ is $f (x) = k [x^{2} - (α + β) x + α . β]$
Where k is any non-zero real number.

The quadratic polynomial whose zeroes are $3 - \sqrt{5}, 3 + \sqrt{5}$ is

$f (x) = k [x^{2} - (3 - \sqrt{5} + 3 + \sqrt{5}) x + (3 - \sqrt{5}) (3 + \sqrt{5})]$

$f (x) = k [x^{2} - 6 x + (3)^{2} - (\sqrt{5})^{2}]$

$f (x) = k [x^{2} - 6 x + (9 - 5)]$

$f (x) = k [x^{2} - 6 x + 4]$

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Form the quadratic polynomial whose zeroes are : 3−√5,3+√5.

The quadratic polynomial whose zeroesareα,β is f(x)=k[x2−(α+β)x+α.β]Where k is any non-zero real number.The quadratic polynomial whose zeroes are 3−√5,3+√5 isf(x)=k[x2−(3−√5+3+√5)x+(3−√5)(3+√5)]f(x)=k[x2−6x+(3)2−(√5)2]f(x)=k[x2−6x+(9−5)]f(x)=k[x2−6x+4]

Form the quadratic polynomial whose zeroes are : $3 - \sqrt{5}, 3 + \sqrt{5}$ .