Question

(14). Find the zeros of the polynomial p(x) = 3 x? -x- 4 and verify the
relationship between the zeros and the coefficients.​

Answer 1

Step-by-step explanation:

$3 {x}^{2} - x - 4 \\ 3 {x}^{2} + 3x - 4x - 4 = 0 \\ 3x(x + 1) - 4(x + 1) = 0 \\ (x + 1)(3x - 4) = 0 \\ x + 1 = 0 \: \: \: \: \: \: \: 3x - 4 = 0 \\ x = - 1 \: \: \: \: \: \: 3x = 4 \\ x = - 1 \: \: \: \: \: \: \: \: x = \frac{4}{3}$

sum of the zeroes = -b/a = -(-1)/3 = 1/3

$= - 1 + \frac{4}{3} \\ = \frac{ - 3 + 4}{3} \\ = \frac{1}{3}$

product of the zeroes = c/a = -4/3

$= - 1 \times \frac{4}{3} \\ = - \frac{4}{3}$

Hope you get your answer