MyQuestionIcon

1

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

Algebraic Expressions

If 2,5 are ...

Question

If $2, 5$ are zeros of polynomial find the polynomial

Open in App

Solution

Let the polynomial be $x^{2} - p x + q = 0$
$2$ is zero of polynomial so $4 - 2 p + q = 0$

$5$ is zero of polynomial so $25 - 5 p + q = 0$
So from the equations $q = 4 + 2 p q = 25 + 5 p 4 + 2 p = 25 + 5 p 21 = 3 p p = 7 q = 4 + 2 (7) q = 18$
So the polynomial is $x^{2} - 7 x + 10$

Suggest Corrections

thumbs-up

0

Similar questions

Q. Verify whether the following are the zeros of the polynomial indicated against them:

p (x) = (x - 2) (x - 5); x = 2, 5

.

Q. If 2 and −2 are two zeros of the polynomial (x⁴ + x³ − 34x² − 4x + 120), find all the zeros of given polynomial.

Q. If α and β are the zeros of the quadratic polynomial f(x) = x² − 1, find the quadratic polynomial whose zeros are

\frac{2 α}{β} and \frac{2 β}{α}

\frac{- 1}{3}

are the zeros of the polynomial 3x³ − 2x² − 7x − 2, find the third zero of the polynomial.

Q. If two zeroes of polynomial

x^{4} + 3 x^{3} - 20 x^{2} - 6 x + 36

\sqrt{2}

- \sqrt{2}

find all other zeros of polynomial.

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Algebraic Expressions

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Algebraic Expressions

Standard X Mathematics

Join BYJU'S Learning Program

CrossIcon