mayankdevnani
  • mayankdevnani
Question in comments .
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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mayankdevnani
  • mayankdevnani
If \(\large \bf a,b \in R\) and \(\large \bf ax^2+bx+6=0,a \neq 0 \) does not have two distinct real roots , then Find:- 1) the minimum possible value of 3a+b 2) the minimum possible value of 6a+b
ParthKohli
  • ParthKohli
\[b^2 < 24a\]Now for inequalities, you always, always, always remember that conditions like minimum hold at boundaries.
mayankdevnani
  • mayankdevnani
yup, i know

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mayankdevnani
  • mayankdevnani
then
ParthKohli
  • ParthKohli
Alright. So we predict that this holds if and only if \(b^2 = 24 a\). Thus\[3a+b = \frac{b^2}{8}+b\]
mayankdevnani
  • mayankdevnani
maine bhi yahi kiya tha
ParthKohli
  • ParthKohli
Now \(b^2/8 + b\) is a quadratic expression and you can find its minimum.
mayankdevnani
  • mayankdevnani
oh ! damn... silly mistake !
mayankdevnani
  • mayankdevnani
multiply galat kiya
ParthKohli
  • ParthKohli
oh lol
mayankdevnani
  • mayankdevnani
8*1=1
mayankdevnani
  • mayankdevnani
lol
mayankdevnani
  • mayankdevnani
by the way, thanks yaar :) @ParthKohli
ParthKohli
  • ParthKohli
no problem
ParthKohli
  • ParthKohli
btw this expression will never actually reach that value
mayankdevnani
  • mayankdevnani
to kaunsi hogi
ParthKohli
  • ParthKohli
I mean the condition is \(b^2 < 24a\) and we've actually taken \(b^2 = 24a\) which is not possible, so \(3a + b\) will never attain its "minimum" value we calculated.
ParthKohli
  • ParthKohli
Actually the condition is \(b^2 \le 24a\) lol. I skipped the part about two distinct roots.
mayankdevnani
  • mayankdevnani
|dw:1450095360096:dw|
ParthKohli
  • ParthKohli
Yes it will attain that value.
mayankdevnani
  • mayankdevnani
you forgot this condition
ParthKohli
  • ParthKohli
What condition?
mayankdevnani
  • mayankdevnani
b^2=4ac
mayankdevnani
  • mayankdevnani
|dw:1450095441887:dw|
ParthKohli
  • ParthKohli
Yeah, yeah, because I only read the question as "if this polynomial does not have real roots".
mayankdevnani
  • mayankdevnani
oh !
mayankdevnani
  • mayankdevnani
lekin main to sabse bada pagal hoon, question hi solve nhi kr paaya

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