Question

Write the following equation in the form ax² + bx + c = 0, then write the values of a, b, c for each equation. (x-1)²=2x+3

Answer 1

QUADRATIC EQUATION :
An equation of degree 2 is called a quadratic equation.
General form of Quadratic equation :
ax² + bx + c , where a,b,c are constants and a≠0.

SOLUTION:
GIVEN :
(x - 1)² = 2x +3
x² + 1² - 2x×1 = 2x +3
[(a-b)²= a²+b² -2ab]
x² -2x -2x + 1 -3= 0
x² - 4x - 2= 0

On comparing with General form of Quadratic equation : ax² + bx + c = 0
Here, a = 1, b = - 4, c = -2

Hence , the value of a = 1, b = - 4, c = - 2.

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Answer 2

Solution:-

given by quadratic equation:-
${(x - 1)}^{2} = 2x + 3 \\ {x}^{2} + 1 - 2x = 2x + 3 \\ {x}^{2} + 1 - 2x - 2x - 3 = 0 \\ {x}^{2} - 4x - 2 = 0 \\ at \: the \: compare \: with \: genral \: formula \: of \: quadratic \: equation \: \\ a {x}^{2} + bx + c = 0 \\ we \: have \: \\ a = 1 \\ b = - 4 \\ c = - 2 \\ hence \: the \: value \: of \: a \: b \: c \: are \: 1 \: - 4 \: - 2.$
(a , b , c ) = ( 1 , -4 , -2) ans


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