Question

Exam.01.12.2016)
136. If x^4 + 2x^3 + ax^2 + bx + 9 is a
perfect square, where a and b are
positive real numbers, then the
values of a and b are
(1) a = 5, b = 6
(2) a = 6, b = 7
(3) a = 7, b= 6
(4) a = 7, b = 8
(SSC CGL Tier-II Online
Exam.01.12.2016)​

Answer 1

not understand write proper questions

Answer 2

Answer:

c

Step-by-step explanation:

$let \: \\ {x}^{4} + {2x}^{3} + {ax}^{2} + bx + 9 \\ = {( {px}^{2} + qx + r)}^{2} \\ {( {px}^{2} + qx + r)}^{2} = {p}^{2} {x}^{4} {2pqx}^{3} \\ since \: \\ {x}^{2} (2pr + {q}^{2} ) + 2qrx + {r}^{2}$

• by equating coefficient of
• $x$
• we get,
• ${p}^{2} = 1 \\ pq = 1 \\ {r}^{2} = 9 \\ a = 2pr + {q}^{2} \\ b = 2qr$
• since it is given that both
• $a$
• and
• $b$
• are positive real numbers, you will see
• $p = 1 = q \\ r = 3$
• thus,
• $a = 7$
• and
• $b = 6$

please mark my answer as brainliest