Question

If α & β are the zeroes of the polynomial 9X
2 + 12X + 4, then find the
value of α + β + αβ

Answer 1

Given:-

• α & β are the zeroes of the polynomial 9x² + 12x + 4

To Find:-

• Value of α + β + αβ

Solution:-

Comparing the given equation with the standard equation i.e. ax² + bx + c = 0 we get,

• a = 9
• b = 12
• c = 4

Sum of Zeroes = $\dfrac{-b}{a}$

$\impliesα + β = \dfrac{-12}{9}$

${\boxed{\impliesα + β = \dfrac{-4}{3}}}$

Product of Zeroes = $\dfrac{c}{a}$

${\boxed{\impliesαβ = \dfrac{4}{9}}}$

Putting values in α + β + αβ,

$= \dfrac{-4}{3} + \dfrac{4}{9}$

$= \dfrac{-12+4}{9}$

$= \:\:\:\:\dfrac{-8}{9}$

Hence, The Value of α + β + αβ is -8/9.

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Answer 2

Hey dear !!

___________________________

==> In the equation ,

p(x) = 9y² + 12y + 4

We have to find the value of α+β + αβ

We have ,

a = 9

b = 12

c = 4

We know that,

α + β = -b/a

= -12/9

= -4/3

Also,

αβ = c/a

= 4/9

A.T.Q

α + β + αβ

∴ The value of α+β + αβ => -8/9

Thanks !