Question

If $\alpha$ and $\beta$ are the roots of the equation $2x^2-3x-5=0$, Find ${\alpha }^2+{\beta }^2$

• A. $\frac{9}{4}$
• B. $\frac{29}{4}$
  
• C. $\frac{4}{6}$
• D. None of these

Answer 1

The correct option is B $\frac{29}{4}$

$\Rightarrow$ $\alpha$ and $\beta$ are the roots of the equation $2x^2-3x-5=0$.

$\Rightarrow$ $2x^2-3x-5=0$

$\Rightarrow$ $2x^2-5x+2x-5=0$

$\Rightarrow$ $x(2x-5)+1(2x-5)=0$

$\Rightarrow$ $(2x-5)(x+1)=0$

$\Rightarrow$ $x=\frac{5}{2}$ and $x=-1$

$\therefore$ $\alpha =\frac{5}{2}$ and $\beta =-1$

$\Rightarrow$ ${\alpha }^2+{\beta }^2$

$\Rightarrow$ ${\left(\frac{5}{2}\right)}^2+(-1{)}^2$

$\Rightarrow$ $\frac{25}{4}+1$

$\Rightarrow$ $\frac{25+4}{4}$

$\Rightarrow$ $\frac{29}{4}$