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the equation 5x^2+(9 +4p)x+2p^2 = 0 and 5x+9=0 are satisfied with same value of x. find the value of p​

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student-name Rohan asked in Math

the equation 5x^2+(9 +4p)x+2p^2 = 0 and 5x+9=0 are satisfied with same value of x. find the value of p

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student-name Varna Salunke answered this

29 helpful votes in Math, Class XII-Science

5x+9=0

5x=(-9)

x= -9/5 ------ ------ -------- --- ------ ----a

putting a in the other equation.

5(-9/5)^2+(9+4p)(-9/5)+2p^2=0

5(81)/25 + 2p^2 + 9(-9/5) +4p(-9/5)=0

81/5 +2p^2 -81/5 - 36p/5=0

2p^2 - 36p/5=0

10p^2 -36p=0

We now need to solve this equation.

We can use any method.

D= b^2 - 4ac

= (-36)^2

p = <-b +-(D)^1/2>/2a

= <36+ - (-36)^1/2>/2 x 10

= 36+ - 36 / 20

p= 0 and p= 72/20 = 3.6

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