Prove that $4$ and $1$ are the zeros of the quadratic polynomial $p (x) = x^{2} - 5 x + 4$ . Also verify the relationship between the zeros and the coefficients of $p (x)$

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Solution

$P (x) = x^{2} - 5 x + 4$
$= x^{2} - 4 x - x + 4$
$= x (x - 4) - (x - 4)$
$= (x - 1) (x - 4)$
$∴ z e r o s o f p (x) a r e x = 1 a n d x = 4$
$s u m o f z e r o s = 1 + 4 = 5 = - ((\frac{c o e f f i c i e n t o f x}{c o e f f i c i e n t o f x^{2}}))$
$p r o d u c t o f z e r o s = 1 \times 4 = ((\frac{c o n s t a n t t e r m}{c o e f f i c i e n t o f x^{2}}))$
hence verified

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