Question

Q1 derived the formula for the quadratic equation ax + bx+c = 0, (a=0)
(A) Brahmagupta
(B) Sridharacharya
(C) Euclid
(D) Thales​

Answer 1

Answer:

Option (B)

Step-by-step explanation:

Corrected Question:-

Who derived the formula for solving the quadratic equation ax²+bx+c = 0 ,where a≠0 ?

Proof :-

The standard quadratic equation is ax²+bx+c = 0

On dividing by a both sides then

=> (ax²+bx+c)/a = 0/a

=> (ax²/a)+(bx/a)+(c/a) = 0

=> x² +(bx/a) + (c/a) = 0

=> x²+(2/2)(bx/a) +(c/a) = 0

=> x²+(2bx/2a) +(c/a) = 0

=> x²+2(bx/2a) + (c/a) = 0

=> x² +2(b/2a)x = -c/a

=> x²+2x(b/2a) = -c/a

On adding (b/2a)² both sides then

=> x²+2x(b/2a)+(b/2a)² = (-c/a)+(b/2a)²

=> [x+(b/2a)]² = (-c/a)+(b²/4a²)

Since, (a+b)² = a²+2ab+b²

=> [x+(b/2a)]² = (-4ac+b²)/(4a²)

=> [x+(b/2a)]² = (b²-4ac)/(4a²)

=> x+(b/2a) = ±√[(b²-4ac)/(4a²)]

=> x+(b/2a) = ±[{√(b²-4ac)}/(2a)]

=> x = ±[{√(b²-4ac)}/(2a)] -(b/2a)

=> x = ±[{√(b²-4ac)}-b]/(2a)

=> x = [-b±√(b²-4ac)]/(2a)

Therefore, the roots are

[-b+√(b²-4ac)]/(2a) and [-b-√(b²-4ac)]/(2a).

This formula is known as Quadratic Formula .

This is derived by Indian Mathematician Sridharacharya.

Answer 2

Step-by-step explanation:

Answer:

Option (B)

Step-by-step explanation:

Corrected Question:-

Who derived the formula for solving the quadratic equation ax²+bx+c = 0 ,where a≠0 ?

Proof :-

The standard quadratic equation is ax²+bx+c = 0

On dividing by a both sides then

=> (ax²+bx+c)/a = 0/a

=> (ax²/a)+(bx/a)+(c/a) = 0

=> x² +(bx/a) + (c/a) = 0

=> x²+(2/2)(bx/a) +(c/a) = 0

=> x²+(2bx/2a) +(c/a) = 0

=> x²+2(bx/2a) + (c/a) = 0

=> x² +2(b/2a)x = -c/a

=> x²+2x(b/2a) = -c/a

On adding (b/2a)² both sides then

=> x²+2x(b/2a)+(b/2a)² = (-c/a)+(b/2a)²

=> [x+(b/2a)]² = (-c/a)+(b²/4a²)

Since, (a+b)² = a²+2ab+b²

=> [x+(b/2a)]² = (-4ac+b²)/(4a²)

=> [x+(b/2a)]² = (b²-4ac)/(4a²)

=> x+(b/2a) = ±√[(b²-4ac)/(4a²)]

=> x+(b/2a) = ±[{√(b²-4ac)}/(2a)]

=> x = ±[{√(b²-4ac)}/(2a)] -(b/2a)

=> x = ±[{√(b²-4ac)}-b]/(2a)

=> x = [-b±√(b²-4ac)]/(2a)

Therefore, the roots are

[-b+√(b²-4ac)]/(2a) and [-b-√(b²-4ac)]/(2a).

This formula is known as Quadratic Formula .

This is derived by Indian Mathematician Sridharacharya.

$answer}$