Question

If α and β are the zeroes of the quadratic polynomial
f(x) =3x 2 − 5x − 2 , then find the value of α2β + αβ2

Answer 1

$\huge\boxed{ \mathbb\red{❥A} \green{n} \mathbb\blue{S} \purple{w} \mathbb \orange{E} \pink{r}} \:</p><p>$

▪️α+β= -b/a

▪️⇒ -(-5)/4

▪️=5/4  

 

▪️αβ= c/a

▪️=-1/4

▪️so α²β+β²α

▪️=αβ(α+β)  (on taking α and β common)

▪️putting value of αβ and α+β

▪️-1/4×5/4

▪️=-5/16

Hopes it help you✌️✌️

Answer 2

$answer$

Hey there!

If α , β are the zeroes of 3x² + 5x + 2

then ,

α + β = -5/3

αβ = 2/3

We \: know \: that , \\ \underline{\underline{ If \: ax^2 + bx + c \: is \: a \: quadratic \: polynomial \: in \: x \: whose \: roots \: are \: p, q }}

\boxed{Sum \: of \: roots = p + q = \frac{-b}{a} , Product \: of \: roots = p*q = \frac{c}{a} }

Now,

1/α + 1/β

= β + α / αβ

= -5/3 / 2/3

= -5/2

Therefore, Value of 1/α + 1/β = -5/2