Complete question 14 (a, b) by using S4 Math quadratic equation.

$4/Math/Ch 1/Quadratic Equations in One Unknown/ExIE/HW06/P.3 14. The figure shows a sequence of diagrams formed by black dots. 8:. Ist diagram 2nd diagram 3rd diagram 4th diagram The number of black dots in the nth diagram is given by n(n + 1) 2 (a) Which diagram has 105 black dots? (b) Is it possible to form a diagram consisting of 254 black dots? Explain your answer. [Hints: Solve n(n +1=254. Check whether the equation has a positive integral root or not.] 2