If the equation ax2+2bx+3c=0 and 3x2+8x+15=0 have a common root, where a,band c are the lengths of the sides of a△ABC, then sin2⁡A+sin2⁡B+sin2⁡C is equal to

Discriminant o{ the equation 3x2+8x+15=0 is given byD=64−180=−116<0so  it , roots are imaginary and therefore roots are conjugate to each other. Therefore, one common root means both the roots are common.∴     a3=2b8=3c15⇒ a3=b4=c5=k  (say), k≠0Now, a2 + b2 = c2⇒ΔABC isrightangled. ∴ sin2⁡A+sin2⁡B=sin2⁡C⇒sin2⁡A+sin2⁡B+sin2⁡C=2sin2⁡C=2sin2⁡90∘=2