Question

plz solve q 5 . fast fast fast.​

Answer 1

Solution:-

$\rm \: eq = 2 {x}^{3} + a {x}^{2} + 11x + a + 3 \: is \: divisible \: by \: (2x - 1)$

To find

$\rm \: value \: of \: a$

Now take

$\rm \to \: 2x - 1 = 0$

$\to\rm \: 2x = 1$

$\boxed{ \rm \to \: x = \dfrac{1}{2} }$

Now put the value of x on given equation

$\to \rm \: 2 {x}^{3} + a {x}^{2} + 11x + a + 3 = 0$

$\rm \to \: 2 \times \bigg( \dfrac{1}{2} \bigg)^{3} + a \times \bigg( \dfrac{1}{2} \bigg)^{2} + 11 \times \bigg( \dfrac{1}{2} \bigg)^{} + a + 3 = 0$

$\rm \: \to \dfrac{2}{8} + \dfrac{a}{4} + \dfrac{11}{2} + a + 3 = 0$

Taking lcm

$\to \rm \: \dfrac{2 + 2a + 44 + 8a + 24}{8} = 0$

$\to \rm \: 2 + 2a + 44 + 8a + 24 = 0$

$\to \rm \: 70 + 10a = 0$

$\rm \to \: 10a = - 70$

$\rm \: a = - 7$

Answer :- a = - 7

Answer 2

Answer :- a = - 7 this is right! :Dd