If two zeroes of the polynomial x2-6 x2-26 x2-138 x-35 are 2 x -3- Find other zeroes-

(2 ±√(3)) are factors So, {x (2+√(3))} and {x (2 √(3))} are factors So, (r 2 √(3)) and (x 2+√(3)) are factors So, (r 2)^2 (√(3))^2 will divide the polynomial x^ ...

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Standard X

Mathematics

Zeroes of a Quadratic Polynomial

If two zeroes...

Question

If two zeroes of the polynomial $x^{2} - 6 x^{2} - 26 x^{2} + 138 x - 35 a r e 2 x \sqrt{3}$ . Find other zeroes.

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Solution

$(2 \pm \sqrt{3})$ are factors
So, ${x - (2 + \sqrt{3})} a n d {x - (2 - \sqrt{3})}$ are factors
So, $(r - 2 - \sqrt{3}) a n d (x - 2 + \sqrt{3})$ are factors
So, $(r - 2)^{2} - (\sqrt{3})^{2}$ will divide the polynomial $x^{2} - 4 x + 1$ will divide
Now

So $x^{2}$ - 2x - 35 will be factors
So $x^{2}$ - 7x + 5x - 35
x(x - 7) + 5(x - 7)
(x - 7) (x + 5) will be factors
So x = 7 8x =-5 will be other two factor

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If two zeros of the polynomial x*4-6x*3-26x*2+138x-35are 2±√3,find other zeros

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If two zeroes of the polynomial x2−6x2−26x2+138x−35 are 2x√3. Find other zeroes.

If two zeroes of the polynomial $x^{2} - 6 x^{2} - 26 x^{2} + 138 x - 35 a r e 2 x \sqrt{3}$ . Find other zeroes.