prove that quadratic equation ax^2+bx+c =-b+-√b^2 …
CBSE, JEE, NEET, CUET
Question Bank, Mock Tests, Exam Papers
NCERT Solutions, Sample Papers, Notes, Videos
Posted by Vishvajit Yadav 5 years, 4 months ago
- 1 answers
Test
Related Questions
Posted by Sahil Sahil 1 year, 3 months ago
- 2 answers
Posted by Kanika . 6 days, 9 hours ago
- 1 answers
Posted by Hari Anand 5 months, 1 week ago
- 0 answers
Posted by Parinith Gowda Ms 2 months, 2 weeks ago
- 1 answers
Posted by Vanshika Bhatnagar 1 year, 3 months ago
- 2 answers
Posted by Parinith Gowda Ms 2 months, 2 weeks ago
- 0 answers
myCBSEguide
Trusted by 1 Crore+ Students
Test Generator
Create papers online. It's FREE.
CUET Mock Tests
75,000+ questions to practice only on myCBSEguide app
Gaurav Seth 5 years, 4 months ago
Quadratic Formula Derivation
Consider the equation ax2+bx+c = 0, a ≠ 0.
Dividing the equation by a gives,
x2+ b/a x+c/a = 0
By using method of completing the square, we get
(x+b/2a)2 – (b/2a)2 + c/a = 0
(x+b/2a)2 – [(b2-4ac)/4a2]= 0
(x+b/2a)2 = (b2-4ac)/4a2
Roots of the equation are found by taking the square root of RHS. For that b2-4ac should be greater than or equal to zero.
When b2-4ac ≥ 0,
(x + b2a) = ± b2 − 4ac√2a
x = −b ± b2 − 4ac√2a —-(1)
Therefore roots of the equation are, −b + b2 − 4ac√2a and −b − b2 − 4ac√2a
The equation will not have real roots if b2-4ac < 0, because square root is not defined for negative numbers in real number system.
Equation (1) is a formula to find roots of the quadratic equation ax2+bx+c = 0, which is known as quadratic formula.
0Thank You