Question

Find the quadratic polynomial whose sum and product
of its zeroes are 2/7 and -3/7 respectively

Answer 1

Given,

sum of zeros = 2/7

Product of zeros = -3/7

» -b/a = 2/7

or, a = 7 and b =-2 [a and b are coefficients of the polynomial respectively]

Again,

c/a = -3/7 » c=-3

Therefore polynomial is

7x^2 -2x-3 = 0.

Answer 2

Answer:

$7 {x}^{2} + 2x - 3 = 0$

Step-by-step explanation:

$\alpha + \beta = \frac{2}{7} \\ \alpha \beta = - \frac{ 3}{7}$

where alpha and beta are the zeroes.

$p(x) = k( {x}^{2} + ( \alpha + \beta )x + \alpha \beta )\\ 0 = k( {x}^{2} + ( \frac{2}{7} )x - \frac{3}{7} ) \\ k \: remains \: constant \\ multiply \: both \: sides \: by \: 7 \\ 0 = 7 {x}^{2} + 2x - 3$