Question

The quadratic equation $2x^2-7x-5=0$ has roots α and β. Match Column I with Column II. Column I Column II

A. $\alpha +\beta$	P. $-2.5$
B. $\alpha \beta$	Q. $3.5$
C. ${\alpha }^2+{\beta }^2$	R. $-\frac{7}{5}$
D. $1/\alpha +1/\beta$	S. $17.25$

• A. A - Q, B - P, C - S, D - R
• B. A - P, B - Q, C - S, D - R
• C. A - P, B - Q, C - R, D - S
• D. A - S, B - R, C - A , D - P

Answer 1

The correct option is A A - Q, B - P, C - S, D - R

$\alpha +\beta =-\frac{(-7))}{2}=3.5$

$\alpha \beta =-\frac{(-5)}{2}=-2.5$

For ${\alpha }^2+{\beta }^2,$ we need to recall that

${\alpha }^2+{\beta }^2=(\alpha +\beta {)}^2-2\alpha \beta =(3.5{)}^2-2(-2.5)=17.25$

$\frac{1}{\alpha }+\frac{1}{\beta }=\frac{(\alpha +\beta )}{\alpha \beta }=\frac{3.5}{-2.5}=-\frac{7}{5}$