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Question
If x = 3 is one root of the quadratic equation 2x2 + px + 30 = 0, find the value of p and the other root of the quadratic equation.
Solution
Given, x = 3 is the root of quadratic equation
2x2 + px + 30 = 0
∴ 2(3)2 + p(3) + 30 = 0
⇒ 18 + 3p + 30 = 0
⇒ 3p = – 48
⇒ p = – 16
Now, the quadratic equation is 2x2 – 16x + 30 = 0
⇒ x2 – 8x + 15 = 0
⇒ x2 – 3x – 5x + 15 = 0
⇒ x(x – 3) – 5(x – 3) = 0
⇒ (x – 3) (x – 5) = 0
⇒ x – 3 = or x – 5 = 0
⇒ x = 3 or x = 5
Hence, the other root of quadratic equation is 5.
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