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Question
If the roots of x2 – px + 4 = 0 are equal, the value (values) of p is ______.
Options
4 and – 4
4
– 4
4 or – 4
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Solution
If the roots of x2 – px + 4 = 0 are equal, the value (values) of p is 4 or – 4.
Explanation:
Given quadratic equation be
x2 – px + 4 = 0 ...(1)
On comparing equation (1) with
ax2 + bx + c = 0
We have a = 1; b = – p and c = 4
Since equation (1) has equal roots
∴ D = 0
`\implies` b2 – 4ac = 0
`\implies` (– p)2 – 4 × 1 × 4 = 0
`\implies` p2 – 16 = 0
`\implies` p2 = 16
`\implies` p = ± 4
`\implies` p = 4 or – 4
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