If two zeros of the polynomial f x - x 4-6 x 3-26 x 2-138 x -35 are 2 -3- find other zeros-A- 6-5B- 7-5C- 5-2D- 4-5

The correct option is B 7, 5If x=2±√(3) then factor of f(x)=x^2 4x+1 {x (2+√(3))}{x (2 √(3))} x^2 4x+1 Now, divide the polynomial f(x) by x^2 4x+1 We get quot ...

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Byju's Answer

Standard X

Mathematics

Zeroes of a Quadratic Polynomial

If two zeros ...

Question

If two zeros of the polynomial f(x) = $x^{4} - 6 x^{3} - 26 x^{2} + 138 x - 35$ are $2 \pm \sqrt{3},$ find other zeros.

6, 5

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7,-5

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5,-2

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4,-5

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Solution

The correct option is B
7,-5

If $x = 2 \pm \sqrt{3}$ then factor of $f (x) = x^{2} - 4 x + 1 {x - (2 + \sqrt{3})} {x - (2 - \sqrt{3})} x^{2} - 4 x + 1$
Now, divide the polynomial f(x) by $x^{2} - 4 x + 1$
We get quotient = $x^{2} - 2 x - 35$
Now, factorize $x^{2} - 2 x - 35$
We get (x-7) (x+5)
We get other zeros, 7, -5

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Similar questions

Q. If two zeros of the polynomial

f (x) = x^{4} - 6 x^{3} - 26 x^{2} + 138 x - 35

are

2 \pm \sqrt{3}

, find ohter zeros. [4 MARKS]

Q. If two zeroes of the polynomial

x^{4} - 6 x^{3} - 26 x^{2} + 138 x - 35

are

2 \pm \sqrt{3},

find other zeroes.

Q. If the zeros of the polynomial

(x^{4} - 6 x^{3} - 26 x^{2} + 138 x - 35)

are

(2 + \sqrt{3})

and

(2 - \sqrt{3})

, find the other zeros.

Q. Find all zeros of

x^{4} - 6 x^{3} - 26 x^{2} + 138 x - 35

, if two zeros are

2 + \sqrt{3}

and

2 - \sqrt{3}

2 + \sqrt{3}

and

2 - \sqrt{3}

are the zeros of

p (x) = x^{4} - 6 x^{3} - 26 x^{2} + 138 x - 35

. Find the remaining zeros of

p (x)

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If two zeros of the polynomial f(x) = x4−6x3−26x2+138x−35 are 2±√3, find other zeros.

The correct option is B 7,-5If x=2±√3 then factor of f(x)=x2−4x+1{x−(2+√3)}{x−(2−√3)}x2−4x+1 Now, divide the polynomial f(x) by x2−4x+1 We get quotient = x2−2x−35 Now, factorize x2−2x−35 We get (x-7) (x+5) We get other zeros, 7, -5

If two zeros of the polynomial f(x) = $x^{4} - 6 x^{3} - 26 x^{2} + 138 x - 35$ are $2 \pm \sqrt{3},$ find other zeros.