Function Composition: Solving Quadratic Formulas with Radicals

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SUMMARY

The discussion focuses on solving quadratic formulas involving radicals, specifically the expression (-3x² - 15x - 12)(√5). Participants clarify that the correct approach involves factoring the quadratic and then multiplying the radical by the solutions derived from the factored form. The key takeaway is that to solve a quadratic equation, one must first establish an equation, which is absent in the initial problem statement.

PREREQUISITES
  • Understanding of quadratic equations and their factored forms
  • Knowledge of the quadratic formula
  • Familiarity with radical expressions and their properties
  • Basic algebraic manipulation skills
NEXT STEPS
  • Study the quadratic formula and its applications in solving equations
  • Learn how to factor quadratic expressions effectively
  • Explore the properties of radicals and their operations
  • Practice problems involving multiplication of polynomials by radicals
USEFUL FOR

Students studying algebra, mathematics educators, and anyone seeking to enhance their understanding of quadratic equations and radical expressions.

dance_sg
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Homework Statement



(-3x^2-15x-12)(√5)

Homework Equations



Quadratic formula?

The Attempt at a Solution


hmm, i know how to solve the first set of bracets, but what do i do with the radical? how do i multiply it to the polynomial?
 
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all you have to do is multiply it to the two solutions
so say the factored quadratic is (x-4)(x+4), so the solutions are 4 and -4. just multiply the rad5 to those two answers.
 
dance_sg said:

Homework Statement



(-3x^2-15x-12)(√5)

Homework Equations



Quadratic formula?

The Attempt at a Solution


hmm, i know how to solve the first set of bracets, but what do i do with the radical? how do i multiply it to the polynomial?

What are you trying to do here? About all you can do with what you've provided is factor the quadratic or multiply the quadratic by sqrt(5). You are not "solving" the first set of brackets - to solve an equation you first off need an equation, which you don't have.
 

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