Question

please solve question no 1.

Answer 1

Heya dear,
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$given \: polynomial \: is \: p(x) = 8 {x}^{3} - 50 {x}^{2} + 53x - 15$

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$at \: x = 5$
$p(5) = 8 {(5)}^{3} - 50 {(5)}^{2} + 53(5) - 15 \\ = 1000 - 1250 + 265 - 15 \\ = 1265 - 1265 = 0$
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at x = 1/2

$p(x) = 8 {( \frac{1}{2} )}^{3} - 50 {( \frac{1}{2} )}^{2} + 53( \frac{1}{2} ) - 15 \\ = 1 - \frac{25}{2} + \frac{53}{2} - 15 \\ = \frac{2 - 25 + 53 - 30}{2} \\ = \frac{55 - 55}{2} = 0$
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at x = 3/4

$p(x) = 8 {( \frac{3}{4} )}^{3} - 50 {( \frac{3}{4}) }^{2} + 53( \frac{3}{4} ) - 15 \\ = \frac{27}{8} - \frac{225}{8} + \frac{159}{4} - 15 \\ = \frac{27 - 225 + 318 - 120}{8} \\ \frac{345 - 345}{8} = 0$

So, 5, 1/2, 3/4 are the zeroes of polynomial p (x).

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