Question

Plz tell the middle term splitting of 2x² + 7/2x + 3/4

Answer 1

$\huge\bold\blue{Question:}$

The middle term splitting of $\bold{2x^{2}+\frac{7x}{2}+\frac{3}{4}}$

$\bold\red{\underline{\underline{Answer:}}}$

$\bold{(x+\frac{3}{2})(2x+\frac{1}{2})}$

$\bold\orange{Explanation:}$

$\bold{The \ given \ quadratic \ polynomial \ is}$

$\bold{2x^{2}+\frac{7x}{2}+\frac{3}{4}}$

$\bold{Here, \ a=2 \ b=\frac{7}{2}, \ c=\frac{3}{4}}$

$\bold{Multiply \ a \ and \ b}$

$\bold{2×\frac{3}{4}}$

$\bold{Let \ find \ two \ terms \ whose \ multiplication}$

$\bold{equals \ to \frac{6}{4} \ and \ addition}$

$\bold{equals \ to \ middle \ term \ i.e. \frac{7}{2}}$

$\bold{\frac{6}{2} \ and \frac{1}{2} \ are \ the \ required \ terms}$

$\bold{\frac{6}{2}×\frac{1}{2}=\frac{6}{4}}$

$\bold{\frac{6}{2}+\frac{1}{2}=\frac{7}{2}}$

$\bold\green{\underline{\underline{Solution}}}$

$\bold{2x^{2}+\frac{7x}{2}+\frac{3}{4}}$

$\bold{=2x^{2}+\frac{6x}{2}+\frac{1x}{2}+\frac{3}{4}}$

$\bold{=2x(x+\frac{3}{2})+\frac{1}{2}(x+\frac{3}{2})}$

$\bold{=(x+\frac{3}{2})(2x+\frac{1}{2})}$