prove that quadratic equation ax^2+bx+c =-b+-√b^2 -4ac

1.	prove that quadratic equation ax^2+bx+c =-b+-√b^2 -4ac
Answer» Quadratic Formula DerivationConsider the equation\xa0ax2+bx+c\xa0= 0, a ≠ 0.Dividing the equation by a gives,\xa0x2+ b/a x+c/a\xa0= 0By using method of completing the square, we get(x+b/2a)2\xa0– (b/2a)2\xa0+ c/a = 0(x+b/2a)2\xa0– [(b2-4ac)/4a2]= 0(x+b/2a)2\xa0= (b2-4ac)/4a2Roots of the equation are found by taking the square root of RHS. For that b2-4ac\xa0should be greater than or equal to zero.When b2-4ac ≥ 0,(x\xa0+\xa0b2a)\xa0=\xa0±\xa0b2\xa0−\xa04ac√2ax\xa0=\xa0−b\xa0±\xa0b2\xa0−\xa04ac√2a\xa0—-(1)Therefore roots of the equation are,\xa0−b\xa0+\xa0b2\xa0−\xa04ac√2a\xa0and\xa0−b\xa0−\xa0b2\xa0−\xa04ac√2aThe 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\xa0ax2+bx+c\xa0= 0, which is known as quadratic formula.

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