If a and 1 - a are the zeroes of P x -4 x 2-2 x - k -4Find k

Let the given polynomial be p(x) = 4x^2 − 2x +(k − 4) Given α and 1/α are zeros of the given polynomial Product of zeroes = (c/a) That is ( α ×1/α) = (k − 4)/4 ...

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Mathematics

Formation of a Quadratic Equation From It's Roots

If a and 1 / ...

Question

If α and $\frac{1}{α}$ are the zeroes of

P(x)=4x²-2x+(k-4),

Find k.

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Solution

Let the given polynomial be p(x) = 4 $x^{2}$ -2 $x$ +(k-4)
Given, α and $\frac{1}{α}$ are zeros of the given polynomial
We know that product of zeroes = $\frac{c}{a}$
( α × $\frac{1}{α}$ ) = $\frac{(k - 4)}{4}$
⇒ 1 = $\frac{(k - 4)}{4}$
⇒ 4 = (k − 4)
∴ k = 8

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If α and 1α are the zeroes of P(x)=4x2-2x+(k-4), Find k.

Let the given polynomial be p(x) = 4x2 -2x +(k-4) Given, α and 1α are zeros of the given polynomialWe know that product of zeroes = ca ( α ×1α ) =(k−4)4 ⇒ 1 = (k−4)4 ⇒ 4 = (k − 4) ∴ k = 8

If α and $\frac{1}{α}$ are the zeroes of

P(x)=4x²-2x+(k-4),

Find k.

Let the given polynomial be p(x) = 4 $x^{2}$ -2 $x$ +(k-4)
Given, α and $\frac{1}{α}$ are zeros of the given polynomial
We know that product of zeroes = $\frac{c}{a}$
( α × $\frac{1}{α}$ ) = $\frac{(k - 4)}{4}$
⇒ 1 = $\frac{(k - 4)}{4}$
⇒ 4 = (k − 4)
∴ k = 8