Given y-x4 - 2x3 - 4x2 - 3x - 5- find the values y at x-2-

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Standard IX

Mathematics

Factor Theorem

Given y=x4 ...

Question

Given $y = x^{4} - 2 x^{3} + 4 x^{2} - 3 x + 5,$ find the values y at $x = \pm 2$ .

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Solution

Consider the given polynomial,
$y = x^{4} - 2 x^{3} + 4 x^{2} - 3 x + 5$

Now, when putting $x = 2$
$y = {(2)}^{4} - 2 {(2)}^{3} + 4 {(2)}^{2} - 3 (2) + 5$
$y = 16 - 16 + 16 - 6 + 5$
$y = 15$

Now, when $x = (- 2)$
$y = {(- 2)}^{4} - 2 {(- 2)}^{3} + 4 {(- 2)}^{2} - 3 (- 2) + 5$
$y = 16 - 16 + 16 + 6 + 5$
$y = 27$

Hence, value of $y$ at $x = 2$ is $15$
value of $y$ at $x = (- 2)$ is $27$

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Given y=x4−2x3+4x2−3x+5, find the values y at x=±2.

Consider the given polynomial,y=x4−2x3+4x2−3x+5Now, when putting x=2y=(2)4−2(2)3+4(2)2−3(2)+5y=16−16+16−6+5y=15Now, when x=(−2)y=(−2)4−2(−2)3+4(−2)2−3(−2)+5y=16−16+16+6+5y=27Hence, value of y at x=2 is 15 value of y at x=(−2) is 27

Given $y = x^{4} - 2 x^{3} + 4 x^{2} - 3 x + 5,$ find the values y at $x = \pm 2$ .