Step 3 : x2 + b/ax [1b/2a]2 = -c/a [1b/2a]2 [Therefore;adding [1b/2a]2 both sides]
Step 4: [x+ b/2a]²=b2-4ac/4a
Step 5: If b2-4ac≥0, then by taking the square roots, we get
x+b/2a=+/-√b²-4ac/2a
therefore,x=-b+/-√b²-4ac/2a
So, the roots of ax² + bx + c = 0 are -b+√b2-4ac/ 2a
and -b-√b2-4ac 2a,if b²-4ac ≥ 0.
If b2-4ac<0, the equation will have no real roots. (Why?)
Thus, if b2-4ac≥0, then the roots of the quadratic equation ax + bx+c=0 are given by
-b±√b2-4ac/2a
This formula for finding the roots of a quadratic equation is known as the quadratic formula.
Let us consider some examples by using quadratic formula.
Example-8. Solve Q. 2(i) of Exercise 5.1 by using the quadratic formula.
Solution: Let the breadth of the plot be x metres.
Then the length is (2x+1) metres
Since area of rectangular plot is 528 m²,
we can write x(2x+1)=528,
ie., 2x²+x-528=0.
This is in the form of ax + bx + c=0, where a=2,b=1, c=-528.
So, the quadratic formula gives us the solution as
pg no-118
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