Question

what is the answer of 2 (i) no. question . please solve it being cool . the question is marked on photo.

Answer 1

Answer:

The value of $\frac{a{\alpha}^2}{b\alpha+c}+\frac{a{\beta}^2}{b\beta+c} \:is\:-2$

Step-by-step explanation:

$since\:\alpha\:and\:\beta\:are\:roots\;of\:ax^2+bx+c=0$,

we have

$a{\alpha}^2+b\alpha+c=0.......(1) \\\\a{\beta}^2+b\beta+c=0.......(2)$

From (1)

$a{\alpha}^2=-(b\alpha+c)\\\\\frac{a{\alpha}^2}{b\alpha+c}=-1.......(3)$

similarly from (2)

$\frac{a{\beta}^2}{b\beta+c}=-1......(4)$

Adding (3) and (4)

$\frac{a{\alpha}^2}{b\alpha+c}+\frac{a{\beta}^2}{b\beta+c} \\\\=-1-1\\\\=-2$