Question

11. What must be added to make x^4 + 6x³ + 19x² + 30x a perfect square?

a) 10 c) 30 b) 25 d) 49​

Answer 1

Hello,
Answer b: 25

Explanation:

`x^4+6x^3+19x^2+30x+a=(x^2+bx+c)^2\\=x^4+2bx^3+b^2x^2+c^2+2cx^2+2bcx\\\\\Longrightarrow\ \left\{\begin{array}{ccc}2b&=&6\\b^2+2c&=&19\\2bc&=&30\\a&=&c^2\\\end{array}\right.\\\\\Longrightarrow\ \left\{\begin{array}{ccc}b&=&3\\c&=&(30)/(2*3)=5\\9+2*5&=&19\\a&=&5^2\\\end{array}\right.`

We must add 25

Answer b) 25