Question

Show that 2and -1/3are zeroes of the polynomial 3x2-5x-2

Answer 1

Step-by-step explanation:

the given equation is

$3 {x}^{2} - 5x - 2$

and zeros of the given equation is

$x = 2 \: and \: x = - \frac{1}{3}$

from zeros we can write as

$x - 2 = 0 \:and \: x + \frac{1}{3} = 0$

now multiply both equation we get,

$(x - 2)(x + \frac{1}{3} ) = 0$

${x}^{2} + \frac{x}{3} - 2x - \frac{2}{3 } = 0$

${x}^{2} - \frac{5x}{3} - \frac{2}{3} = 0$

taking LCM we get

$\frac{ 3{x}^{2} - 5x - 2 }{3} = 0$

$3 {x}^{2} - 5x - 2 = 0$

hence we get the given equation, so that

$x = 2 \: and \: x = - \frac{1}{3}$

are the zeros of the polynomial