Question

if alpha and 1/alpha are the zeroes of the polynomial 3x2 +x +(k-2) find k

Answer 1

GIVEN :

$\alpha$ and $\frac{1}{\alpha}$ are the zeroes of the polynomial $3x^2+x+(k-2)$

TO FIND :

The value of k in the given polynomial.

SOLUTION :

Given polynomial is $3x^2+x+(k-2)$

Given that $\alpha$ and $\frac{1}{\alpha}$ are the zeroes of the polynomial $3x^2+x+(k-2)$

Compare the given polynomial $3x^2+x+(k-2)$ with $ax^2+bx+c$ we get the values a = 3 , b = 1  and c = k - 2 ,

$Product of the zeroes = \frac{c}{a}$

Substitute the values in the formula we get,

$Product of the zeroes=\alpha\times \frac{1}{\alpha}=\frac{k-2}{3}$

$1=\frac{k-2}{3}$

3=k-2

k-2=3

k=3+2

∴ k=5

∴ the value of k in the given polynomial is 5.

Answer 2

Sol :-

To find -

value of k

Explanation -

α x 1/α =c/a

In polynomial 3x² + x + (k - 2),

a = 3 , b = 1 , c = k - 2

.'. α x 1/α =c/a

⇒ 1 = k - 2 / 3

⇒ k - 2 = 3

⇒ k = 2 + 3

⇒ k = 5  

.'. the value ok k in 3x^2 + x + (k - 2) is 5  

Additional information :-

.'. polynomial is 3x² + x + 5 - 2

                       ⇒ 3x² + x + 3