Sum

Find the zeros of the quadratic polynomial 4x^{2} - 9 and verify the relation between the zeros and its coffiecents.

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#### Solution

We have

4x^{2} - 9 = (2x)^{2} - 3^{2} = (2x -3)(2x + 3)

So, the value of 4x^{2} - 9 is 0, when

2x - 3 = 0 or 2x + 3 = 0

i.e., when x = `3/2` or x = `(-3)/2`

Therefore the zeros of 4x^{2} - 9 are `3/2` and `(-3)/2`

Sum of the zeros

`= 3/2-3/2 = 0 = -((0))/4 = -["coefficient of x"/("coefficient of "x^2)]`

Product of the zeros

`= 3/2 xx (-3)/2 = (-9)/4 = ["coefficient of x"/("coefficient of "x^2)]`

Concept: Relationship Between Zeroes and Coefficients of a Polynomial

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