State
whether ( 2x- 3) square =4x+7x-1is a quadratic equations or not? justify
Answers
Step-by-step explanation:
(2x-3)^2=4x+7x-1
4x^2+9-12x=4x+7x-1
4x^2+9-12x-4x-7x+1=0
4x^2+9+1-23x=0
4x^2-23x+10=0
Conditions necessary for a quadratic equation:-
Coefficient of x^2 cannot be zero
But,
In the above equation we see that coefficient of x^2 is 4 which is not equal to zero
Therefore,(2x-3)^2=4x+7x-1 is a quadratic equation
Answer:
A simple technique to just identify whether a the given equation is quadratic or no is that check whether there is only one term of square on either LHS or RHS...
Now in this example only on one side there is a squared term (LHS) hence there is no term in the RHS to cancel the squared term in LHS so this is a quadratic equation...
If u want to prove it mathematically then..
Expand (2x - 3)^2 = 4x^2 + 9 - 12x
Now equate this with 4x + 7x - 1
Therefore,
4x^2 + 9 - 12x = 4x + 7x - 1
4x^2 - 12x -11x +9 - 1 = 0
4x^2 - 23x + 8 = 0
As there is a square term still existing... Hence it is a quadratic equation...
Hope it helps...