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 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard X

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.

Open in App

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

Suggest Corrections

260

Similar questions

Q. If

α and β

are the zeroes of

p (x) = 4 x^{2} + 10 x + k

such that

α^{2} + β^{2} + α β = \frac{21}{4}

, then k =

- 5

is one of the zeroes of

2 x^{2} + p x - 15

, zeroes of

p (x^{2} + x) + k

are equal to each other. Find the value of

k

α

and

\frac{1}{α}

are zeroes of polynomial

4 x^{2} - 2 x + k + 7

. Find the value of

k

Q. Question 4
Find the value of k, if

x = 2, y = 1

is a solution of the equation

2 x + 3 y = k .

Q. If one zero of the polynomial

p (x) = (k + 4) x^{2} + 13 x + 3 k

is reciprocal of the other, then k is equal to

Join BYJU'S Learning Program

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