[" If "sin alpha" and "log alpha" ore the reets "],[" of the "eg" ase "+6x+c" of them "],[" frome that "a^(2)+2ac=b^(2)" ."]

If sin alpha and cos alpha are the roots of the equation ax^(2)+bx+c=0 then prove that a^(2)+2ac=b^(2)

If alpha and alpha^(2) are the roots of the equation x^(2) - 6x + c = 0 , then the positive value of c is

If" " alpha " and " beta " satisfy the equation " a cos 2 theta + b sin 2 theta = c " then show that " cos^(2) alpha + cos ^(2)beta =1 + (ac)/(a^(2) + b^(2))

If sin alpha,cos alpha are the roots of equation cx^(2)+bx+a=0, then show that b^(2)-2ac-c^(2)=0

If alpha and beta the roots of the equation ax^(2)+bx+c=0 then the sum of roots of the equation a^(2)x^(2)+(b^(2)-2ac)x+b^(2)-4ac=0(i)-(alpha^(2)-beta^(2))(ii)(alpha+beta)^(2)-2 alpha beta(iii)alpha^(2)beta+beta^(2)alpha+2 alpha beta(iv)(alpha^(2)+beta^(2))

If alpha,beta are the roots of the equation ax^(2)+bx+c=0, then prove that (alpha)/(beta)+(beta)/(alpha)=(b^(2)-2ac)/(ac)

If the expression 4sin5 alpha cos3 alpha cos2 alpha is expressed as the sum of threes sines then two of them are sin 4 alpha and sin10 alpha. The third one is (a)sin8 alpha(b)sin6 alpha(d)sin5 alpha(d)sin12 alpha

If alpha and beta be two roots of the equation a cos theta+ b sin theta=c , show that sin alpha+ sin beta=(2bc)/(a^(2)+b^(2)) ,sin alpha sin beta =(c^(2)-a^(2))/(a^(2)+b^(2)) and tan (alpha+ beta)=(2ab)/(a^(2)-b^(2))