Question

Find the quadratic ploynomial whose zeros are 2/3 and -6. Verify the relation between the coefficient and the zeros of polynomial.

Answer 1

Answer:

(x-2/3)(x+6)=0

3x^2+16x-12=0

put x=2/3,-6 it will result in 0.

Answer 2

$k( {x}^{2} - x( \frac{2}{3} - 6) + \frac{2}{3} \times - 6) \\ k( {x}^{2} - x( \frac{2 - 18}{3} ) + - 4) \\ k( {x}^{2} - x( - \frac{16}{3} ) - 4) \\ k( {x}^{2} + \frac{16x}{3} - 4) \\ 3( {x}^{2} + \frac{16x}{3} - 4) \\ 3 {x}^{2} + 16x - 12$