Question

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

Answer 1

The value of is zero when x − 4 = 0 or x + 2 = 0, i.e., when x = 4 or x = −2

Therefore, the zeroes of are 4 and −2.

Sum of zeroes =

Product of zeroes
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The value of 4s² − 4s + 1 is zero when 2s − 1 = 0, i.e.,

Therefore, the zeroes of 4s² − 4s + 1 areand.

Sum of zeroes =

Product of zeroes

The value of 6x² − 3 − 7x is zero when 3x + 1 = 0 or 2x − 3 = 0, i.e., or

Therefore, the zeroes of 6x² − 3 − 7x are.

Sum of zeroes =

Product of zeroes =

The value of 4u² + 8u is zero when 4u = 0 or u + 2 = 0, i.e., u = 0 or u = −2

Therefore, the zeroes of 4u² + 8u are 0 and −2.

Sum of zeroes =

Product of zeroes =

The value of t² − 15 is zero when or , i.e., when

Therefore, the zeroes of t² − 15 are and.

Sum of zeroes =

Product of zeroes =

The value of 3x² − x − 4 is zero when 3x − 4 = 0 or x + 1 = 0, i.e., when or x = −1

Therefore, the zeroes of 3x² − x − 4 are and −1.

Sum of zeroes =

Product of zeroes