Let $x^{2} + x + 1$ is a factor of ${5 x}^{2} + A x + B$ . Then:

A = 5, B = 5

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A = 5, B = 0

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A = 0, B = - 5

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A = - 5, B = 0

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Solution

The correct option is A $A = 5, B = 5$
$x^{2} + x + 1$ is a factor of ${5 x}^{2} + A x + B$

$5 x^{2} + A x + B = a (x^{2} + x + 1) = a x^{2} + a x + a$
$\Rightarrow a = 5$
Then, $A = a = 5, B = a = 5$
Therefore, answer is $A = 5, B = 5$

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Let x2+x+1 is a factor of 5x2+Ax+B. Then:

The correct option is A A=5,B=5x2+x+1 is a factor of 5x2+Ax+B5x2+Ax+B=a(x2+x+1)=ax2+ax+a⇒a=5Then, A=a=5,B=a=5 Therefore, answer is A=5,B=5

Let $x^{2} + x + 1$ is a factor of ${5 x}^{2} + A x + B$ . Then:

The correct option is A $A = 5, B = 5$
$x^{2} + x + 1$ is a factor of ${5 x}^{2} + A x + B$

$5 x^{2} + A x + B = a (x^{2} + x + 1) = a x^{2} + a x + a$
$\Rightarrow a = 5$
Then, $A = a = 5, B = a = 5$
Therefore, answer is $A = 5, B = 5$