Question

If two zeros of the polynomial x square - 5 x + k are the reciprocal of each other then find the value of k

Answer 1

Answer:

$\large{\underline{\boxed{\sf k = 1}}}$

Step-by-step explanation:

Given that ;

One zero of the polynomial (x² - 5x + k) is reciprocal to other.

x² - 5x + k, where

• a = 1
• b = - 5
• c = k

Let the zeroes of the polynomial be α and 1/α.

Product of zeroes = $\bf \dfrac{c}{a}$

⇒ α * 1/α = k/1

⇒ 1 = k

⇒ k = 1

Hence, the value of k is 1.

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$\large{\underline{\underline{\mathfrak{\heartsuit \: Extra \: Information: \: \heartsuit}}}}$

For a quadratic polynomial ax² + bx + c, the zeroes are α and β, where

• α + β = - b/a
• αβ = c/a

Answer 2

Answer:

k = 1

Step-by-step explanation:

x² - 5x + k

If one zero is reciprocal to other,

Product of zeroes = c/a

$\alpha \times \frac{1}{ \alpha } = \frac{k}{1} \\ \\ 1 = k \\ \\ k = 1$

Hence, the answer is 1.