EXERCISE 3.1

EXERCISE . . If the sides of a cubic box are increased by , , units respectively to form a cuboid, then the volume is increased by cubic units. Find the volume of the cuboid. . Construct a cubic equation with roots (i) , , and (ii) , , and − (iii) and . . If α , β and γ are the roots of the cubic equation x , form a cubic equation whose roots are (i) α , β , γ (ii) α , β , γ (iii) −α , −β , −γ . Solve the equation if the product of two roots is . . Find the sum of squares of roots of the equation - - Theory of Equations . Solve the equation x if it is given that two of its roots are in the ratio : . If α β , and γ are the roots of the polynomial equation ax bx cx , find the value of βγ