Question

find the zeros of the polynomial and verify the relationship between the zeros and their coefficients 3 X square + 4 x minus 4..
Please help its urgent ​

Answer 1

Step-by-step explanation:

$3 {x}^{2} + 4x - 4 = 0$

$3 {x}^{2} + 6x - 2x - 4 = 0$

$3x(x + 2) - 2(x + 2)$

$(3x - 2)(x + 2) = 0$

$3x - 2 = 0 \: \: \: \: or \: \: \: \: x + 2 = 0$

$x = \frac{2}{3} \: \: \: \: or \: \: \: \: x = - 2$

Let alpha and beta be the zeroes of polynomial,

$\alpha = \frac{2}{3} \: \: \: \: and \: \: \: \: \beta = - 2$

We know that,

$sum \: ot \: zeroes = - \frac{b}{a}$

$\frac{2}{3} + ( - 2) = \frac{ - 4}{3}$

$\frac{2 - 6}{ \not \: 3 } = \frac{ - 4}{ \not 3}$

$- 4 = - 4$

$product \: of \: zeroes = \frac{c}{a}$

$\frac{2}{3} \times - 2 = \frac{ - 4}{3}$

$\frac{ - 4}{ 3} = \frac{ - 4}{ 3}$

Hence verified