Question

If one root of the quadratic equation ax2 +bx+ c=0 is half of the other root, show that b2=9ac/2​

Answer 1

Answer:

Step-by-step explanation:

$The \ given \ equation \ is :\\\\ax^2 +bx+c=0\\\\Let \ one \ root \ is \ 2m \ then \ other \ one\ is \ m\\\\Thus \ sum \ of \ roots \ = m+2m=-\frac ba\\\\3m= -\frac ba\\\\m=-\frac {b}{3a}------------(1)$

$The \ product \ of \ roots\\\\m(2m)=\frac ca\\\\2m^2 =\frac ca\\\\Putting \ the \ value \ of \ m from\ (1)\\2(-\frac{b}{3a})^2=\frac ca\\\\2(\frac {b^2}{9a^2} ) = \frac ca\\\\2ab^2=9a^2c\\\\b^2 =\frac {9a^2c}{2a}\\\\\\Hence\, \ b^2 =\frac {9ac}{2}\\\\HENCE \ PROVED$

Answer 2

Answer: step by step solved answer in imagep

Step-by-step explanation: