Math, asked by sudeep347, 11 months ago

If 2/3 and – 3 are the roots of the equation px² + 7x + q = 0, find the values of p and q.​

Answers

Answered by sajathasajatha5
5

Answer:

x=2/3 and x=-3

(x-2/3)(x+3)=0

x^2+3x-2/3x+(-2)=0

x^2+(9x-2x)/3-2=0

x^2+7/3x-2=0

Answered by Brenquoler
43

 { \red{ \bf{   Let's\:  substitute \:the\: given\: value}}}

 { \red{ \bf{    x = 2/3 \:in \:the \:expression,\: we \:get:}}}

px² + 7x + q = 0

p(2/3)² + 7(2/3) + q = 0

4p/9 + 14/3 + q = 0

 { \red{ \bf{   }}}

By taking LCM

4p + 42 + 9q = 0

 { \red{ \bf{   4p + 9q = – 42----------(1)}}}

 { \red{ \bf{Now,   }}}

 { \red{ \bf{  substitute\: the\: value\: x = -3 }}}

 { \red{ \bf{   in\: the \:expression,\: we\: get:}}}

px² + 7x + q = 0

p(-3)² + 7(-3) + q = 0

9p + q – 21 = 0

9p + q = 21

 { \red{ \bf{   q = 21 – 9-----------(2)}}}

 { \red{ \bf{   By \: substituting \: the\: value\: of \:q\: in\: eqn. (1),}}}

 { \red{ \bf{   We\: get:}}}

4p + 9q = – 42

4p + 9(21 – 9p) = -42

4p + 189 – 81p = -42

189 – 77p = -42

189 + 42 = 77p

231 = 77p

p = 231/77

 { \red{ \bf{  p = 3 }}}

 { \red{ \bf{ Now, \:substitute\: the\: value\: of\: p\: in \:equation (2),  }}}

 { \red{ \bf{  We \: get: }}}

q = 21 – 9p

= 21 – 9(3)

= 21 – 27

 { \red{ \bf{ = -6  }}}

 { \red{ \bf{ ∴ Value\: of \:p \: is \: 3 \: and \: q \: is \: -6.  }}}

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