Question

If a,b,c,d are the roots of the equation
3x⁴ – 8x³ + 2x² – 9=0 then Eab =​

Answer 1

Correct Question :

$\tt\dagger \: if \: a ,\: b ,\: c ,\: and \:.d \: are \: the \: roots \: of \: equation \\ \tt{\: \: 3 {x}^{4} - 8 {x}^{3} + 2 {x}^{2} - 9 = 0.}$

$\tt then ,\: \sum ab.$

AnsWer :

2/3.

Solution :

Let Compare with General Equation,

$\tt \dagger \: \: \: a {x}^{4} + b {x}^{3} + c {x}^{2} + dx + e = 0.$

$\tt where \:a s, \: \red{ a, \: b, and , \: c \neq 0.}$

Now,

We have equation,

$\tt 3 {x}^{4} - 8 {x}^{3} + 2 {x}^{2} - 9 = 0.$

And,

Here Summation Sign show that Sum of all products of Zeros.

i.e,

$\tt \: abcd = \frac{c}{a} = \frac{Coefficient \: of \: {x}^{2}}{Coefficient \: of \: {x}^{4} }$

$\tt \mapsto \sum ab = \frac{c}{a}$

$\tt \mapsto \sum ab = \frac{2}{3}$

Therefore, the value of summation ab be 2/3.