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Question
If x = p is a solution of the equation x(2x + 5) = 3, then find the value of p.
Solution
Given, x = p and x(2x + 5) = 3
Substituting the value of p, we get
p(2p + 5) = 3
⇒ 2p2+ 5p – 3 = 0
⇒ 2p2 + 6p – p – 3 = 0 ...`{(∵ 2xx(-3) = -6),(∴ -6 = 6xx(-1)),(5 = 6 - 1):}}`
⇒ 2p(p + 3) –1(p + 3) = 9
⇒ (p + 3)(2p – 1) = 0
EIther p + 3 = 0,
then p = –3
or
2p – 1 = 0,
then 2p = 1
⇒ p = `(1)/(2)`
∴ p = `(1)/(2)`, –3.
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