plz solve q 5 . fast fast fast.
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plz solve q 5 . fast fast fast.
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Solution:-
[tex] \rm \: eq = 2 {x}^{3} + a {x}^{2} + 11x + a + 3 \: is \: divisible \: by \: (2x - 1)[/tex]
To find
[tex] \rm \: value \: of \: a[/tex]
Now take
[tex] \rm \to \: 2x - 1 = 0[/tex]
[tex] \to\rm \: 2x = 1[/tex]
[tex] \boxed{ \rm \to \: x = \dfrac{1}{2} }[/tex]
Now put the value of x on given equation
[tex] \to \rm \: 2 {x}^{3} + a {x}^{2} + 11x + a + 3 = 0[/tex]
[tex] \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[/tex]
[tex] \rm \: \to \dfrac{2}{8} + \dfrac{a}{4} + \dfrac{11}{2} + a + 3 = 0[/tex]
Taking lcm
[tex] \to \rm \: \dfrac{2 + 2a + 44 + 8a + 24}{8} = 0[/tex]
[tex] \to \rm \: 2 + 2a + 44 + 8a + 24 = 0[/tex]
[tex] \to \rm \: 70 + 10a = 0[/tex]
[tex] \rm \to \: 10a = - 70[/tex]
[tex] \rm \: a = - 7[/tex]
Answer :- a = - 7
Answer :- a = - 7 this is right! :Dd