Question

Find the quadratic equation .​

Answer 1

Question :

$x^2 + 2x - 3 = 0.$

Solution :

$\underline{\bold{Given:}}$

• $x^2 + 2x - 3 = 0.$

$\underline{\bold{To\:Find:}}$

• The roots of the equation.

$\implies x^2 + 2x - 3 = 0 \\ \implies x^2 + (3 - 1)x - 3= 0\\ \implies x^2 + 3x - x - 3 = 0 \\ \implies x(x + 3) - 1(x + 3) = 0 \\ \implies (x + 3)(x - 1) = 0 \\\implies x=0-3\:or\:x=0+1\\\implies x=-3\: or\:x=1$

$\fbox{\green{\therefore{The\: roots\: of\: the\: equation\:are\:x=-3 \:and\:x=1}}}$

$\underline{\bold{Verification:}}$

Taking x=-3 as the root of the equation :

$\implies x^2 + 2x - 3 = 0 \\\implies (-3)^2+2\times(-3)-3=0\\\implies 9+(-6)-3=0\\\implies 9-6-3=0\\\implies 9-9=0\\\implies 0=0$

Taking x=1 as the root of the equation :

$\implies x^2 + 2x - 3 = 0 \\\implies (1)^2+2\times 1-3=0\\\implies 1+2-3=0\\\implies 3-3=0\\\implies 0=0$

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