Question

Question 6 Find the value of a if (x - 1) is a factor of 2x² + ax + 2. a​

Answer 1

Step-by-step explanation:

Here,x+1 is a factor of $\tt \: p(x) = {2x}^{2} +a x + 2.$

$\color{red} \tt \therefore \: \: \: \: \: \: \: p \bigg(1 \bigg) = 0$

$\pmb{ \color{darkcyan} \begin{array}{l} \tt \implies \: 2 \bigg(1 \bigg) {}^{2} + a \bigg(1 \bigg) + 2 = 0 \\ \tt \implies \: 2 \times 1 + a + 2 = 0 \\ \tt \implies \: 2 + a + 2 = 0 \\ \tt \implies \: 4 + a = 0 \\ \implies \: \boxed{\boxed{ \tt a = - 4}}\end{array}}$

Answer 2

Answer:

The answer is $a=-\dfrac{2}{3}$

Step-by-step explanation:

Factor theorem: If $x-a$ is a factor of a polynomial P(x), then P$(a)=0$

Here given $x-1$ is a factor of $P(x)=2x^2+ax+2a$

                     $\Rightarrow P(1)=0\\\Rightarrow 2(1)^2+a(1)+2a=0\\\Rightarrow 2+a+2a=0\\\Rightarrow 3a=-2\\\Rightarrow a=-\dfrac{2}{3}$