# If the equations 5x square + (9+4p)x + 2p square = 0 and 5x + 9 = 0 are satisfied by the same value of x . Find the value of p.

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Equations 5x² + (9+4p)x + 2p² = 0 and 5x + 9 = 0 are satisfied by the same value of x.

5x+9 = 0

⇒ 5x = -9

⇒ x = -9/5

now x = -9/5 is a solution of 5x² + (9+4p)x + 2p² = 0

5x² + (9+4p)x + 2p² = 0

⇒ 5(-9/5)² + (9+4p)(-9/5) + 2p² = 0

⇒ 5*81/25 -81/5 - 36p/5 + 2p² = 0

⇒ 81/5 - 81/5 -36p/5 + 2p² = 0

⇒ 2p² = 36p/5

⇒ p = 36/5*2 or p = 0

⇒ p = 18/5 or p=0

Values of p are 0 and 18/5

5x+9 = 0

⇒ 5x = -9

⇒ x = -9/5

now x = -9/5 is a solution of 5x² + (9+4p)x + 2p² = 0

5x² + (9+4p)x + 2p² = 0

⇒ 5(-9/5)² + (9+4p)(-9/5) + 2p² = 0

⇒ 5*81/25 -81/5 - 36p/5 + 2p² = 0

⇒ 81/5 - 81/5 -36p/5 + 2p² = 0

⇒ 2p² = 36p/5

⇒ p = 36/5*2 or p = 0

⇒ p = 18/5 or p=0

Values of p are 0 and 18/5

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5x + 9 = 0

x = -9/5

5 x² + 9x + 4 p x + 2 p² = 0

5 * 81/25 - 81/5 -36 p /5 + 2 p² = 0

p² - 18 p/5 = 0

p = 0 or p= 18/5

x = -9/5

5 x² + 9x + 4 p x + 2 p² = 0

5 * 81/25 - 81/5 -36 p /5 + 2 p² = 0

p² - 18 p/5 = 0

p = 0 or p= 18/5