Question

If α,β are the roots of the quadratic equation $x^2$ – (a – 2)x –(a+1) =0, where 'a' is a variable then the least value of ${\alpha }^2$+${\beta }^2$

• A. 3
• B. 5
• C. 7
• D. 9

Answer 1

The correct option is B

5

${\alpha }^2+{\beta }^2$ =$(a-2{)}^2$+2(a+1) =${(a-1)}^2$+5$\ge$5