Question

find the zeroes of the following quadratic polynomials and verify the relation between the zeroes and the coeffients : 3zsquare-2z-1​

Answer 1

answer is in the attachment....

follow my brainly a/c

Answer 2

$p(x) = 3 {z}^{2} - 2z - 1$

TO FIND :- Zeros of the polynomial and verify the relationship between them.

$3 {z}^{2} - 2z - 1 = 0 \\ \\ \implies 3 {z}^{2} - 3z + z - 1 =0 \\ \\ \implies 3z(z - 1) + 1(z - 1) = 0 \\ \\ \implies (z - 1)(3z + 1) = 0 \\ \\ \implies z = 1 \: or \: \frac{ - 1}{3}$

Let one zero of the polynomial be alpha and other be beta.

Now we shall check the relationship ,

α + β = -b/a

αβ = c/a

$\alpha + \beta = 1 + \frac{ - 1}{3} \\ \\ = \frac{2}{3} = \frac{ - ( - 2)}{3} = \frac{ - b}{a}$

$\alpha \beta = 1 \times \frac{ - 1}{3} = \frac{ - 1}{3} \\ \\ = \frac{ - 1}{3} = \frac{c}{a} \: (ans)$