Question

Find zeroes of polynomial 9m - 16m-4.​

Answer 1

The equation will contain an equality sign. So, in the absence of equality sign, you should use the word quadratic polynomial or at least polynomial in place of 'equation'.

I will take it as quadratic polynomial (4m+1)x^2 - 6mx + 4

The polynomial becomes a perfect square, if the zeros are equal.That happens when the discriminant 'b^2 - 4ac' = 0

In the given polynomial, a = 4m + 1, b = -6m, c = 4

Hence, (-6m)^2 - 4(4m + 1)(4) = 0. Simplifying, we get 9 m^2 - 16m - 4 = 0. So, m = 2 or -2/9.

Hence the polynomial (4m+1)x^2 - 6mx + 4 becomes a perfect square if m = 2 or -2/9.

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