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If `tantheta and sectheta` are the roots of `a x^2+b x+c=0,` then prove that `a^4=b^2(b^2-4ac)dot`

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If tanthetaa n dsectheta are the roots of a x^2+b x+c=0, then prove that a^4=b^2(b^2 - 4ac)dot

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Let alpha and beta be the roots of the equationa ax^2 + bx + c = 0 and alpha + gamma and beta + gamma be the roots of Ax^2 + Bx + C = 0. Then prove that A^2(b^2 - 4ac) = a^2(B^2 - 4AC).

If the ratio of the roots of the equation x^2+p x+q=0 are equal to ratio of the roots of the equation x^2+b x+c=0 , then prove that p^2c=b^2qdot

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if alpha , beta are root of ax^2+bx+c=0 then (1/alpha^2+1/beta^2)^2 (a) (b^(2)(b^(2)-4ac))/(c^(2)a^(2)) (b) (b^(2)(b^(2)-4ac))/(ca^(3)) (c) (b^(2)(b^(2)-4ac))/(a^(4)) (d) (b^(2)-2ac)^2/(c^(4))

If a\ a n d\ b are roots of the equation x^2-x+1=0 then write the value of a^2+b^2dot

alpha,beta are the roots of ax^(2)+2bx+c=0 and alpha+delta,beta+delta are the roots of A x^(2)+2Bx+C=0 , then what is (b^(2)-ac)//(B^(2)-AC) equal to ?

If alpha and beta are the roots of the equation ax^(2)+bc+c=0 then the sum of the roots of the equation a^(2)x^(2)+(b^(2)-2ac)x+b^(2)-4ac=0 is

If a+b+c=0 then check the nature of roots of the equation 4a x^2+3b x+2c=0 where a ,b ,c in Rdot

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