Question

Find the quadratic polynomial whose sum of roots is -1/4 and product is 1/4

Answer 1

Answer:

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Answer 2

Let the zeroes be A and B respectively

We know that,

Sum of the zeroes = -(coefficient of x) / coefficient of x²

=> A + B = -1/4

Product of the zeroes = constant term/ coefficient of x²

=> AB = 1/4

So, the polynomial = x² - (A+B)x + AB

=> x² -(-1)/4 x + 1/4 = 0

=> x² + x/4 + 1/4 = 0

Taking LCM

=> (4x² + x + 1) / 4 = 0

=> 1/4 ( x² + x + 1 ) = 0

=> x² + x + 1 = 0