If ax² + bx + c=0 then prove that: x={ -b ±√(b²-4ac) } /2a . (No spam or useless answers please)
Answers
Answer:
A quadratic equation is of the standard form ax^2+bx+c, a not equal to 0.
Here, a = root 5.
Therefore the above equation is quadratic. (does not matter if the coefficient of x(b), and constant 'c' is zero.
Answer:
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Class 10
>>Maths
>>Quadratic Equations
>>Nature of Roots
>>Prove the root of equation ax^2 + bx + c
Question
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Prove the root of equation ax
2
+bx+c=0 is ⇒x=
2a
−b±
b
2
−4ac
Medium
Solution
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Consider the quadratic equation ax
2
+bx+c
⇒a(x
2
+
a
b
x+
a
c
)=0
⇒x
2
+
a
b
x+
a
c
=0
⇒x
2
+
a
b
x=−
a
c
This can be written as
⇒x
2
+2×
2a
b
x=−
a
c
Add (
2a
b
)
2
on both sides
⇒x
2
+2×(
2a
b
)x+(
2a
b
)
2
=−
a
c
+(
2a
b
)
2
This can be written as
⇒(x+
2a
b
)
2
=
a
−c
+
4a
b
2
⇒(x+
2a
b
)
2
=
4a
2
−4ac+b
2
⇒x+
2a
b
=±
4a
2
−4ac+b
2
⇒x+
2a
b
=±
2a
b
2
−4ac
⇒x=
2a
−b
±
2a
b
2
−4ac
⇒x=
2a
−b±
b
2
−4ac