Question

If the equations $a{x}^2+2bx+3c=0$and 3$x^2+8x+15=0$ have a common root where a,b,c, are lengths of sides of ABC then $si{n}^{2}A$ + $si{n}^{2}B$ + $si{n}^{2}C=$

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

$3x^2+8x+15=0$

$\Delta <0$

$\therefore$ both roots common

$\therefore$ $\frac{a}{3}=\frac{2b}{8}=\frac{3c}{15}$ $\Rightarrow a=3$ $\lambda$, $b=4$ $\lambda$ , $c=5$ $\lambda$

$\therefore$ $\angle$ c = ${90}^{\circ }$ $\Rightarrow$ $A+B$ = ${90}^{\circ }$

$si{n}^{2}A+si{n}^{2}B=si{n}^{2}c=2$