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Question
If the zeroes of the quadratic polynomial ax2 + bx + c, c ≠ 0 are equal, then ______.
Options
c and a have opposite signs
c and b have opposite signs
c and a have the same sign
c and b have the same sign
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Solution
If the zeroes of the quadratic polynomial ax2 + bx + c, c ≠ 0 are equal, then c and a have the same sign.
Explanation:
The zeroes of the given quadratic polynomial ax2 + bx + c where c ≠ 0, are equal.
If coefficient of x2 and constant term have the same sign i.e. c and a have the same sign.
While b i.e., coefficient of x can be positive or negative but not zero.
Consider,
(i) x2 + 4x + 4 = 0
`\implies` (x + 2)2 = 0
`\implies` x = –2, –2
(ii) x2 – 4x + 4 = 0
`\implies` (x – 2)2 = 0
`\implies` x = 2, 2
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