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Question
If one root of the equation 2x² – px + 4 = 0 is 2, find the other root. Also find the value of p.
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Solution
The given quadratic equation is
2x² – px + 4 = 0
one root = 2
Let the other root be a
The sum of the roots 2 + a = `(-(-p))/(2) = p/(2)`
a = `p/(2) - 2` ...(i)
The product of the roots
a x 2 = `(4)/(2) = 2`
⇒ a = 1
Now 2 + a = `p/(2)`
⇒ 2 + 1 = `p/(2)`
⇒ p = 6.
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