Question

find the roots of the following quadratic equation by factorisation methaod ;a^2b^2x^2+b^2x-a^2x-1=0find the root of the following quadratic equation a square B Square X square + b square x minus A square x minus 1 is equal to zero by factorization method

Answer 1

Simplifying a2b2x2 + b2x + -1a2x + -1 = 0 Reorder the terms: -1 + a2b2x2 + -1a2x + b2x = 0 Solving -1 + a2b2x2 + -1a2x + b2x = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + a2b2x2 + -1a2x + 1 + b2x = 0 + 1 Reorder the terms: -1 + 1 + a2b2x2 + -1a2x + b2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + a2b2x2 + -1a2x + b2x = 0 + 1 a2b2x2 + -1a2x + b2x = 0 + 1 Combine like terms: 0 + 1 = 1 a2b2x2 + -1a2x + b2x = 1 Add '-1b2x' to each side of the equation. a2b2x2 + -1a2x + b2x + -1b2x = 1 + -1b2x Combine like terms: b2x + -1b2x = 0 a2b2x2 + -1a2x + 0 = 1 + -1b2x a2b2x2 + -1a2x = 1 + -1b2x Reorder the terms: -1 + a2b2x2 + -1a2x + b2x = 1 + -1b2x + -1 + b2x Reorder the terms: -1 + a2b2x2 + -1a2x + b2x = 1 + -1 + -1b2x + b2x Combine like terms: 1 + -1 = 0 -1 + a2b2x2 + -1a2x + b2x = 0 + -1b2x + b2x -1 + a2b2x2 + -1a2x + b2x = -1b2x + b2x Combine like terms: -1b2x + b2x = 0 -1 + a2b2x2 + -1a2x + b2x = 0

Answer 2

Solution is in the given attachment.

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Let's see some related terms ;

Factorisation : It is the term that means to differ the factors of a given expression.

Linear equations in two variables :

▪️A linear equation in two variables has infinitely many solutions.

▪️Standard form of a linear equation in two variables is « ax + by + c = 0 », where a and b are coefficients of x and y respectively and she is a constant.

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Thanks for the question!