Question

26. Find the value of k which the roots of the
equation 3x^2 - 10k + k = 0 are reciprocol of
each other
ICBSE 2019)​

Answer 1

Question :-

Find the value of k for which the roots of the equation 3x² - 10x + k = 0 are reciprocal of each other.

Answer :-

Let one zero be α

It is given that, other zero is reciprocal -

Other zero = 1 / α

Now, we know that

Product of zeros of quadratic equation = c/a

For the equation 3x² - 10x + k :-

→ Product of zeros = k / 3

Also,

→ Product of zeros = α × 1 / α

→ Product of zero = 1

Hence,

→ k/3 = 1

→ k = 3

Value of k = 3

Answer 2

Given:

• Equation = 3x² - 10k + k = 0
• Zeroes of the equation are reciprocal of each other.

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To find:

• Value of k.

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Solution:

$\dag\mathcal{Let\: one\: zero\: of\: the\: equation\: be\: \alpha} \\ \\ \mathcal{Then,\: another\: zero\: will\: be\: \dfrac{1}{\alpha}}$

⠀

We know that,

• Product of zeroes = $\sf{\dfrac{c}{a}}$

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$\sf\dashrightarrow{\alpha \times \dfrac{1}{\alpha} = \dfrac{k}{3}}$

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$\sf\dashrightarrow{1 = \dfrac{k}{3}}$

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$\sf\dashrightarrow{3 = k}$

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$\bf\dashrightarrow{\purple{k = 3}}$

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⠀⠀$\underline{\sf{Thus,\: value\: of\: k\: is\: 3}}$