Solve the following equation by factorisation: √3 x2+10x+7√3=0.
By BYJU'S Exam Prep
Updated on: September 25th, 2023
Factorization is a mathematical process of breaking down an expression, equation, or number into its constituent factors. The factors are the individual terms or numbers that, when multiplied together, result in the original expression or number. Factorization is commonly used in various areas of mathematics, including algebra and number theory.
In algebra, factorization involves expressing an algebraic expression as a product of its irreducible factors. For example, the expression x2 – 4 can be factored as (x – 2)(x + 2). This factorization represents the original expression as a product of two binomial factors.
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Solving the equation by factorisation
To solve an equation by factorization, you need to find the factors of the expression on one side of the equation and set each factor equal to zero. By doing this, you can determine the values of the variable that satisfy the equation.
Solution:
To solve the following equation by factorisation: √3x2+10x+7√3=0, follow the below-mentioned steps.
√3x2+10x+7√3=0
x2+10x/√3+7=0
x2+2*5/√3*x+(5/√3)2-25/3+7=0
(x+5/√3)2=4/3
x+5/√3=±2/√3
x=-√3, -7/√3
Therefore, the solutions to the equation √3x2+10x+7√3=0 are x = -√3 and x = -7√3.
Summary:
Solve the following equation by factorisation: √3x2+10x+7√3=0.
The solutions to the equation √3x2+10x+7√3=0 are x = -√3 and x = -7√3. Remember to always check your solutions by substituting them back into the original equation to ensure they satisfy the equation.
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