Answer:
-274
Step-by-step explanation:
First, you find the product of the roots: Since the product of two roots is the third root, we can use Vieta's formulas to find the product of the roots:
[tex]P=(-1)^3*t=-t[/tex]
Secondly, you then have to express the roots in terms of the coefficients. Vieta's formulas also give us:
[tex]S=14,\\T=-26[/tex]
where S is the sum of the roots and T is the sum of the products of the roots taken two at a time.
Thirdly, then use Vieta's formulas to find the greatest value of t: Substituting S and T into the formula for P, we get:
[tex]-t=S^2-3T\\-t=14^2-3*(-26)\\-t=196+78\\t=-274[/tex]
Therefore, the greatest value of t is -274.
