Question

If x-2 is a factor of x³-3x+5a then the value of a is what

Answer 1

Answer:

a=-2/5

Step-by-step explanation:

1st method

x-2)x^3 -3x +5a (x^2+2x+1

x^3 -2x^2 (to substract put-vesignin x^3-2x^2)

_________

2x^2 -3x + 5a

2x^2 -4x

______________

x + 5a

x - 2

________

5a+2

since x-2 is a factor of x³-3x+5a

so 5a+2=0

a= -2/5

2nd method

since x-2 is a factor of x³-3x+5a

so put x=2 in x³-3x+5a=0

8-6+5a=0

2+5a=0

a=-2/5

rakhithakur

Answer 2

$\footnotesize➵\footnotesize \text \blue{\:Given:-}$

$\footnotesize➵\footnotesize \text \red{\:x - 2 is a factor}$

$\:$

$\footnotesize➵\footnotesize \text \blue{\:Find:-}$

$\footnotesize➵\footnotesize \text \red{\:Value of a}$

$\:$

$\footnotesize➵\footnotesize \text \blue{\:Solution:-}$

$\:$

$\footnotesize \text \red{x - 2 = 0}$

$\boxed{ \boxed{\footnotesize \text \blue{x = 2}}}$

$\:$

$\footnotesize \text \red{x³ \: - \: 3x \: + \: 5a = 0}$

$\footnotesize \text \red{2³ \: - 3 × 2 \: + \: 5a = 0}$

$\footnotesize \text \red{8 \: - \: 6 \: + \: 5a = 0}$

$\footnotesize \text \red{2\: + \: 5a = 0}$

$\footnotesize \text \red{ 5a = - 2}$

$\boxed{ \boxed{\footnotesize \text \blue{ a = - 2/5}}}$

$\:$

$\footnotesize \text \red{Factor means} \\\footnotesize \text \blue { \: \: \: \: If you put that value in place of x} \\ \footnotesize \text \red{ \: \: \: \: \: \: \: \: \: It gives value of p(x) = 0}$