Question

If Alpha, beta and gamma are roots of equation x³-x²+7x+2=0, then the equation whose roots are -a,-b,-y is​

Answer 1

Answer:

Let a,b,c be the roots of x3+x+1=0 so we have a+b+c=0,ab+bc+ca=1,abc=−1, so a2+b2+c2=−2 and c3=−c−1

We would explore a transformation from x to y to get the required cubic equation of y. Let

y=(a−b)2=a2+b2−2ab=y=−2−c2+2/c⟹c=31+y

Replacing c by x we get the required transformation x=31+y, putting it in the given x equation, we get:

27(1+y)3+3(1+y)+1=0⟹y3+6y2+9y+31=0,

which is the required cubic equation.

Answer 2

Answer:

The photoelectric effect is the emission of electrons when electromagnetic radiation, such as light, hits a material. Electrons emitted in this manner are called photoelectrons. ... The effect has found use in electronic devices specialized for light detection and precisely timed electron emission.