what is the value of p in the quadratic expression: x^2(4p+1)+x(2p-1)+6=0
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Is any other information about the value of x provided?
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(4p + 1)x^2 +x(2p -1) + 6 =0
this is quadratic equation so, according to quadratic, rule coefficient of x^2 ≠0
e.g 4p +1 ≠0
p ≠ -1/4
also ,
for real value of this quadratic equation,
Discriminant =b^2 -4ac ≥0
(2p -1)^2 -4(4p+1)6≥0
4p^2 -4p +1 -96p -24 ≥0
4p^2 -100p -23 ≥0
{ p-(100+_√(100^2+16×23))/8}≥0
let. this quadratic roots ß and ¢
where ß> ¢
then,
(p-ß)(p-¢) ≥0
p≥ß. and p≤ ¢ and p≠ -1/4
this is quadratic equation so, according to quadratic, rule coefficient of x^2 ≠0
e.g 4p +1 ≠0
p ≠ -1/4
also ,
for real value of this quadratic equation,
Discriminant =b^2 -4ac ≥0
(2p -1)^2 -4(4p+1)6≥0
4p^2 -4p +1 -96p -24 ≥0
4p^2 -100p -23 ≥0
{ p-(100+_√(100^2+16×23))/8}≥0
let. this quadratic roots ß and ¢
where ß> ¢
then,
(p-ß)(p-¢) ≥0
p≥ß. and p≤ ¢ and p≠ -1/4
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