MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Factor Theorem

Obtain all ze...

Question

Obtain all zeros of the polynomial f(x) = x⁴ − 3x³ − x² + 9x − 6, if two of its zeros are $- \sqrt{3} and \sqrt{3}$

Open in App

Solution

We know that if is a zero of a polynomial, then is a factor of .

Since and are zeros of .

Therefore

is a factor of .Now, we divide by to find the other zeros of .

By using division algorithm we have, .

Hence, the zeros of the given polynomials are .

Suggest Corrections

thumbs-up

9

Similar questions

Q.
Obtain all other zeroes of

f (x) = x^{4} - 3 x^{3} - x^{2} + 9 x - 6

if two of its zeroes are

- \sqrt{3}

\sqrt{3}

Q. If polynomial

f (x) = x^{4} - 3 x^{3} - x^{2} + 9 x - 6

has two zeroes as

- \sqrt{3}, \sqrt{3}

find all zeroes of the polynomial

Q. Obtains all other zeroes of

x^{4} - 3 x^{3} - x^{2} + 9 x - 6

, if two of its zeroes are

\sqrt{3}

- \sqrt{3}

If two of the zeroes of the polynomial f (x) = x⁴ - 3x³ - x² + 9x - 6 are - √3 and √3 then all the zeroes are

Q. Find all zeroes of the polynomial if

2

of its zeroes are

\pm \sqrt{3}

.

f (x) = x^{4} - 3 x^{3} - 7 x^{2} + 12

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Factor Theorem

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Standard X Mathematics

Join BYJU'S Learning Program

CrossIcon