Find the zeros of the quadratic polynomial $f (x) = x^{2} - 3 x - 28$ and verify the relationships between the zeros and the coefficients.

x = 7, - 4

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sum of roots

= - 3

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product of roots

= - 28

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x = - 7, 4

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Solution

The correct options are
A $x = 7, - 4$
B product of roots $= - 28$
C sum of roots $= - 3$
$x^{2} - 3 x - 28 = 0 x^{2} - 7 x + 4 x - 28 = 0 x (x - 7) + 4 (x - 7) = 0 (x + 4) (x - 7) = 0 ∴ x = - 4, 7 s u m o f r o o t s = - 4 + 7 = 3 p r o d u c t o f r o o t s = - 4 \times 7 = - 28$

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