Question

if α and β are the zeroes of the polynomial 4x2 - 2x + ( k - 4) and α=1?solution: , find the value of k. ​

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Answer 1

Provided:-

• α and β are the zeroes of the polynomial.
• Equation :- 4x^2 - 2x + (k - 4).

To Find:-

• Value of k.

Solution:-

Compare 4x^2 - 2x + (k - 4) with

ax^2 + bx + c.

Here,

a = 4,

b = -2,

c = k - 4.

★Product of zeroes = c/a

→ α × 1/α = (k - 4) / 4

→ 1 = (k - 4) / 4

→ 4 = k - 4

→ 4 + 4 = k

→ 8 = k

Hence,

• k = 8

Answer 2

Given

• α and β are the zeroes of the polynomial.
• Polynomial 4x² - 2x + ( k - 4)
• α = 1

To find

• Value of k.

Solution

$\sf\pink{⟶}$ Standard form of a polynomial is ax² + bx + c.

★ On comparing

$\begin{lgathered}\begin{lgathered}\begin{lgathered}\tt {\pink{Given}}\begin{cases} \sf{\green{a = 4}}\\ \sf{\blue{b = -2}}\\ \sf{\orange{c = (k - 4)}}\end{cases}\end{lgathered} \:\end{lgathered}\end{lgathered}$

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

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$\tt:\implies\: \: \: \: \: \: \: \: {α × \dfrac{1}{α} = \dfrac{(k - 4)}{4}}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {1 = \dfrac{k - 4}{4}}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {4 = k - 4}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {k = 4 + 4}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {k = 8}$

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