Question

If zeroes of the polynomial 6 x square + 4 x + 2 a are alpha and 1/alpha then the value of a is

Answer 1

Answer

The value of a is 3

$\bf\large\underline{Given}$

The quadratic polynomial is :

• 6x² + 4x + 2a
• α and 1/α are the zeroes of the given polynomial

$\bf\large\underline{To \ Find}$

• The value of a

$\bf\large\underline{Solution}$

Given , the polynomial 6x² + 4x + 2a has the zeroes α and 1/α

We have , from the relationship of the product of the zeroes and coefficients:

$\sf product \: of \: the \: zeroes = \dfrac{constant \: term}{coefficient \: of \: {x}^{2} }$

$\sf \implies \alpha\times \dfrac{1}{\alpha}= \dfrac{2a}{6} \\\\ \sf\implies 1 = \dfrac{2a}{6} \\\\ \sf\implies 2a = 6 \\\\ \sf \implies a = 3$

Thus , the value of a is 3

Answer 2

Given ,

The polynomial 6(x)² + 4x + 2a whose zeroes are " α " and " 1/α "

We know that , the product of zeroes is given by

$\boxed{ \sf{Product \: of \: zeroes = \frac{c}{a} }}$

Thus ,

α × 1/α = 2a/6

1 = 2a/6

a = 6/2

a = 3

Therefore ,

• The value of a is 3