Question

If the roots of \(x^2+ax+b\)=0 are $se{c}^2\Pi /8$ and $cose{c}^2\Pi /8$ ,then which of the following is correct?

• A. a - b =0
• B. a + b =0
• C. 2a = b
• D. a = 2b

Answer 1

The correct option is B

a + b =0

$se{c}^2\Pi /8$ and $cose{c}^2\Pi /8$ are the roots of the quadratic equation $x^2+ax+b$=0

now, sum of roots = $se{c}^2\Pi /8+cose{c}^2\Pi /8$

$\frac{1}{co{s}^2\Pi /8}$ + $\frac{1}{si{n}^2\Pi /8}$ = $\frac{si{n}^2\Pi /8+co{s}^2\Pi /8}{si{n}^2\Pi /8.co{s}^2\Pi /8}$

$\frac{1}{\left(si{n}^2\Pi /8.Co{s}^2\Pi /8\right)}$ = $se{c}^2\Pi /8.cose{c}^2\Pi /8$

=> -a = b

a+b=0