`a^2-b^2-4ac+4c^2`

Factorise : a^(2)-9b^(2)+4c^(2)-25d^(2)-4ac+30bd

Prove that: |-a^2 ab ac ba -b^2 bc ac bc c^2| =4a^2b^2c^2 .

If b^2 - 4ac

Using properties of determinants, prove the following abs{:(a^2, bc, ac +c^2 ),(a^(2) + ab, b^(2),ac ),(ab, b^(2) + bc,c^(2) ):}=4a^(2) b^(2) c^(2) .

If the roots of ax^2+bx+c=0 are real and equal then.......a) b^2-4aclt0 b) b^2-4ac=0 c) b^2-4acgt0 d) Cannot say

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^2, ab, ac),(ab,-b^2,bc),(ac,bc,-c^2)] then det A is equal to (A) 4abc (B) 4a^2b^2c^2 (C) -4abc (D) -4a^2b^2c^2

If the roots of the equation ax^(2)+bx+c=0 are of the form (k+1)/k and (k+2)/(k+1), then (a+b+c)^(2) is equal to 2b^(2)-ac b.a62 c.b^(2)-4ac d.b^(2)-2ac