Question

If a and b are the zeroes of the 5x^2+2x+3 then a^3+b^3

Answer 1

Answer:

82/125

Step-by-step explanation:

let

f(x)= 5x²+2x+3

If a and b are zero's of this polynomial then

a and b will be the root of the quadratic equation

5x²+2x+3=0

now we know that :

$a {x}^{2} + bx + c = 0 \\ \alpha + \beta = - \frac{b}{a} \\ \alpha \beta = \frac{c}{a}$

$where \: \alpha \: and \: \beta \: are \: its \: roots$

a+b=-2/5

ab=3/5

${(a + b)}^{3} = {a}^{3} + {b}^{3} + 3ab(a + b) \\ {a}^{3} + {b}^{3} = (a + b)( {(a + b)}^{2} - 3ab)$

substituting the values of a+b and ab

a³+b³ = (-2/5)((-2/5)²-3(3/5))

=82/125

have a nice day