Find a quadratic polynomial with zeroes -2 and 1/3. – InterviewSolution

1.

Find a quadratic polynomial with zeroes -2 and 1/3.

Answer»

Let the quadratic polynomial be ax² + bx + c, a ≠ 0 and its zeroes be α and β.

Here α = – 2 and β = 1/3

Sum of the zeroes = α + β

= -2 + 1/3 = -5/3

Product of the zeroes = αβ

= 1/3 × (-2) = -2/3

∴ ax² + bx + c is [x² – (α + β)x + αβ]

= [ x²- (-5/3) x + (-2/3)]

the quadratic polynomial will be 3x² + 5x – 2.

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