The solution of the quadratic equation is (ii) 0 and 6. (iii) Imran's father was 30 years old when Imran was born.
Quadratic equation in one variable is generally of the form of ax²+bx+c=0 where x is the variable and a, b and c are constants.
The degree of a quadratic polynomial is 2 and there are 2 solutions for a quadratic equations.
The graph of a quadratic equation is parabolic in shape.
Imran's father is x² years when Imran is x years. So after 4x years:
Imran's father's age=x²+4x
Imran's age=x+4x=5x
Now Imran's father is twice as old as Imran
∴2×(5x)=x²+4x
or, 10x=x²+4x
or, x²-6x=0
Hence the equation reduces to a quadratic equation of the form x²-6x=0.
ii) Solving the quadratic equation:x²-6x=0
Breaking into factors we get:
or, x(x-6)=0
either x=0 or x-6=0 or, x=6
Therefore the solution of the equation is 0,6 .
iii) When x=6 i.e, Imran is 6 years old,
age of his father = x²=6²=36 years.
So when Imran was born 6 years ago age of his father=36-6=30 years old.
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