Question

Solve the quadratie equation x² + 2bx - (a²-b²) = 0

Plss answer this
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Answer 1

Basic Concept Used :-

There are three methods to find the factors of quadratic equation :-

• 1. Method of factorization

• 2. Method of Completing squares

• 3. Using Quadratic Formula

Here, we prefer

• Method of Factorization by Regrouping the terms

Let's solve the problem now!!!

Given Question :-

Solve the quadratic equation :-

$\rm :\longmapsto\: {x}^{2} + 2bx - ( {a}^{2} - {b}^{2}) = 0$

Solution :-

$\rm :\longmapsto\: {x}^{2} + 2bx - ( {a}^{2} - {b}^{2}) = 0$

$\rm :\longmapsto\: {x}^{2} + 2bx - {a}^{2} + {b}^{2} = 0$

$\rm :\longmapsto\: {x}^{2} + 2bx+ {b}^{2} - {a}^{2} = 0$

$\rm :\longmapsto\: {(x + b)}^{2} - {a}^{2} = 0$

$\: \: \: \: \: \: \: \: \: \: \because \: \boxed{ \sf \: {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2}}$

$\rm :\longmapsto\:(x + b + a)(x + b - a) = 0$

$\: \: \: \: \: \: \: \: \: \: \because \: \boxed{ \sf \: {(x + y)}(x - y) = {x}^{2} - {y}^{2}}$

$\bf :\longmapsto\:x = - a - b \: \: \: \: \: or \: \: \: \: x = a - b$

Additional Information :-

Nature of roots :-

Let us consider a quadratic equation ax² + bx + c = 0, then nature of roots of quadratic equation depends upon Discriminant (D) of the quadratic equation.

• If Discriminant, D > 0, then roots of the equation are real and unequal.

• If Discriminant, D = 0, then roots of the equation are real and equal.

• If Discriminant, D < 0, then roots of the equation are unreal or complex or imaginary.

Where,

• Discriminant, D = b² - 4ac