Page 39 - CHAPTER 4 (Quadratic equations)

CHAPTER 4
QUADRATIC EQUATIONS

TYPE-4: Equation of the form (x + a)(x + b)(x + c)(x + d)+k=0 a<b<c<d

and a + d = b + c = s

Method: I (i) Combine the first and the last bracket and second and

2
2
third bracket together to get (x +sx+ad) (x +sx+bc)+k=0
(ii) Put x +sx=t, which reduces the question to (t+ad)(t+bc)+k=0
2
(iii) Solve for t and then solve for x.

OR

II (i) Put t= (x+a)+(x+b)+(x+c)+(x+d) , this will generate an equation reducible
4

to quadratic equation.

(ii) Solve for t and then solve for x.

TYPE 5: Equations of the form √(ax+b)=k or √(ax+b)+√(cx+d)=k or

√(ax+b) +√(cx+d=√(ex+f)

Method: Get rid of the radical signs by squaring to obtain a polynomial

that can be

solved easily. One should be careful of extraneous roots.

39