Question

Help me understand, I am total blank understanding this.

Answer 1

$$\huge \ let, \alpha \ be \ a\ common\ root\ then,$$
$$\huge a\alpha^2+b\alpha+c=0 \ and \ a'\alpha^2+b'\alpha+c'=0$$

$$\huge \ I\ get\ it \ till \ here,\ but\ not\ the\ next\ step.$$

It is written that by solving the above equation we get

$$\huge\frac{\alpha^2}{bc'-b'c}=\frac{\alpha}{ca'-c'a}=\frac{1}{ab'-a'b}$$

How did we get the last step from the two equations, please help.....

Answer 2

both the equations above are equal to ZERO.

Answer 3

@ganeshie8 please help.

Answer 4

Eliminate the \(\Large \alpha^2\) term:
Multiply the first equation by a' and the second equation by a, subtract and solve for \(\Large \alpha\).

Eliminate the \(\Large \alpha\) term:
Multiply the first equation by b' and the second equation by b, subtract and solve for \(\Large \alpha^2\).

Rearrange the two equations to put it in the form in the last step.