Question

If a and b are the zeroes of the polynomials 2xsquare+5x+1 then what is the value of a+b+ab?

Answer 1

Step-by-step explanation:

Given -

• α and β are zeroes of polynomial p(x) = 2x² + 5x + 1

To Find -

Value of α + β + αβ

Here,

a = 2

b = 5

c = 1

As we know that :-

• α + β = -b/a

→ α + β = -5/2

And

• αβ = c/a

→ αβ = 1/2

Then,

The value of α + β + αβ is

→ -5/2 + 1/2

→ -5 + 1/2

→ -4/2

→ -2

Hence,

The value of α + β + αβ is -2

Some related formulas :-

☞ For quadratic polynomial :

• α + β = -b/a
• αβ = c/a

☞ For cubic polynomial :

• α + β + γ = -b/a
• αβγ = -d/a
• αβ + βγ + γα = c/a

Answer 2

$\large{\boxed{\underline{\underline{\bf{\red{Answer:-}}}}}}$

$\implies$ -2

$\large\underline\mathrm{Given:-}$

• a and b are the zeroes of the polynomials p(x) = 2x² + 5x + 1

$\large\underline\mathrm{To \: find}$

• value of α + β + αβ

$\implies$ a = 2

$\implies$ b = 5

$\implies$ c = 1

$\large\underline\mathrm{Solution}$

$\implies$ α + β = -b/a

$\implies$ α + β = -5/2

$\large\underline\mathrm{and,}$

$\implies$ αβ = c/a

$\implies$ αβ = 1/2

$\large\underline\mathrm{The \: value \: of \: α \: + \: β \: + \: αβ \: is}$

$\implies$ -5/2 + 1/3

$\implies$ (-5 + 1)/2

$\implies$ -4/2

$\implies$ -2

$\large\underline\mathrm{hence,}$

$\large\underline\mathrm{The \: value \: of \: α \: + \: β \: + \: αβ \: is \: -2.}$

$\large\underline\mathrm{Hope \: it \: helps \: you \: plz \: mark \: me \: brainlist}$