Question

Express 5x²-15x+1 in the form p(x+q)²+r, where p,q,r ate constants

Answer 1

Answer:

$5\bigg(x-\frac{3}{2}\bigg)^2-\frac{41}{4}$

Step-by-step explanation:

• $5x^2-15x +1$

• $= 5\bigg(x^2-3x +\frac{1}{5}\bigg)$

• $=5\bigg[x^2-2.\frac{3}{2}x +\bigg(\frac{3}{2}\bigg)^2-\bigg(\frac{3}{2}\bigg)^2+\frac{1}{5}\bigg]$

• $=5\bigg[\bigg(x-\frac{3}{2}\bigg)^2+\frac{1}{5}-\frac{9}{4}\bigg]$

• $=5\bigg[\bigg(x-\frac{3}{2}\bigg)^2+\frac{4-45}{20}\bigg]$

• $=5\bigg(x-\frac{3}{2}\bigg)^2-5.\frac{41}{20}$

• $=5\bigg(x-\frac{3}{2}\bigg)^2-5.\frac{41}{20}$

• $=5\bigg(x-\frac{3}{2}\bigg)^2-\frac{41}{4}$