Question

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class 10
maths​

Answer 1

Question :

If one zero of the polynomial f(x) = x² + 7x + 3k is the reciprocal of the other, then what is the value of k ?

Answer:

The required value of k is 1/3

Step-by-step explanation:

Given :

One zero of the polynomial f(x) = x² + 7x + 3k is reciprocal of the other.

To find :

the value of k

Solution :

Let one zero be 'a'

The other zero is reciprocal of the other.

Hence, the other zero = 1/a

To solve this question, we must know the relation between zeroes and coefficients.

★ Sum of zeroes = -(x coefficient)/x² coefficient

★ Product of zeroes = constant term/x² coefficient

Given polynomial is f(x) = x² + 7x + 3k

‣ x² coefficient = 1

‣ x coefficient = 7

‣ constant term = 3k

It is easy to find the value of k by using the product of zeroes relation.

➙  (a) × (1/a) = 3k/1

➙  1 = 3k

➙  k = 1/3

Therefore, the value of k is 1/3.

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