Question

Factorize the polynomial 2x² + 11/2 x+ 24 by splitting middle term.​

Answer 1

       $\underline{\bold{Answer:}}$

       $\text{The polynomial }2x^{2} + \frac{11}{2}x + 24 = 0 \text{ cannot be factorized}$

       $\underline{\bold{Step-by-step-explaination:}}$

       $\text{The given polynomial is }2x^{2} + \frac{11}{2} x + 24 = 0$

       $\text{We can simplify the middle term of the polynomial by multiplying 2}\\\text{on both sides}$

$\implies \boxed{2(2x^{2} + \frac{11}{2}x + 24) = 2(0)}$

$\implies \boxed{4x^{2} + 11x + 48 = 0}$

       $\text{First, let us check the Discriminant}(\delta) \text{ of the polynomial}$

$\implies \boxed{(11)^{2} - 4(4)(48)=\delta}$

$\implies \boxed{121 - 768 = \delta}$

$\implies \boxed{-647 = \delta}$

       $\text{Since, }\delta < 0$

$\implies \text{The roots of the above polynomial are imaginary}$

   $\therefore \text{ The polynomial }2x^{2} + \frac{11}{2}x + 24 = 0 \text{ cannot be factorized}$

Answer 2

Step-by-step explanation:

here is the answer of your question hope it's helpful for you