Mathematics

Problem

Consider the quadratic equation

6x^{2}-19x+15=0

. a. (i) Factorise

6x^{2}-19x+15

into a product of two linear factors. b. (ii) Hence find the roots of the equation. c. (iii) Verify that the sum and the product of the roots satisfy

-\frac{b}{a}

and

\frac{c}{a}

respectively for the quadratic

ax^{2}+bx+c=0