Question

If $sin\theta$
and $cos\theta$ are roots of the equation $a{x}^2+bx+c=0$ then

• A. (a)$(a-c{)}^2=b^2-c^2$
• B. (b)$(a-c{)}^2=b^2+c^2$
• C. (c)$(a+c{)}^2=b^2-c^2$
• D. (d)$(a+c{)}^2=b^2+c^2$

Answer 1

Answer: (D)

(d)$(a+c{)}^2=b^2+c^2$

$sin\theta ,cos\theta$ are the roots of the

equation $a{x}^2+bx+c=0$

$\therefore sin\theta +cos\theta =-b/a$

$sin\theta .cos\theta =c/a$

$si{n}^2\theta +co{s}^2\theta =1$

$\Rightarrow (sin\theta +cos\theta {)}^2-2sin\theta cos\theta =1$

$\Rightarrow (-b/a{)}^2-2c/a=1$

$\Rightarrow b^2-2ac=a^2$

$\Rightarrow a^2+2ac+c^2=b^2+c^2$

$\Rightarrow (a+c{)}^2=b^2+c^2$ [Ans]