Solution of a Quadratic Equation by Factorisation
Consider the following products.
Above example illustrate that whenever the product is 0, at least one of the factors is 0.
Imp: If a and b are numbers, then ab = 0, iff a = 0 or b = 0.
Above principle is used in solving quadratic equation by factorisation. Let given quadratic equation be Let the quadratic polynomial be expressed as product of two linear factors i.e. (px + q) and (rx + s), where p, q, r, s are real numbers and p ¹ 0, r ¹ 0,
Then,
Þ
\ Either or
or rx = –s
or
Following steps are involved in solving a quadratic equation by factorisation.
· Transform the equation into standard form, if necessary.
· Factorise .
· Put each factor containing variable = 0.
· Solve each of the resulting equation.
Solved Problems Based on Solution of a Quadratic Equation by Factorisation
Problem:
Using factorisation, solve following equations.
(i) (ii)
Solution:
(i)
Þ
Þ
Þ
either or
either or
Solution is x = 8, –4
(ii)
or
either or
either or
Solution is
Problem:
Solve :
Solution:
Þ
Þ
Either or
Þ or
Þ or
Hence, are the required solutions.
Problem:
Solve: , a, b are real numbers
Solution:
Þ
[]
Þ
Þ
Þ
Þ either
or
or
either or
Hence, are the required solutions.
Problem:
Solve the following quadratic equation by factorization method:
Solution:
We have,
Þ
Þ
Þ
either
or,
Þ
or,
Problem:
Solve the following quadratic equations by factorization method:
Solution:
We have,
Þ
Þ
Þ
Þ
Þ –ab =
Þ
Þ
Þ
Þ
Þ or,
Þ or,
\ Solution is x = -a, -b