By definition of polynomials, the polynomial 3 · x² + 24 · x + 15 represents a <em>quadratic</em> equation whose roots are - 5 and - 3 and whose <em>leading</em> coefficient is 3.
<h3>How to derive a quadratic equation based on given roots</h3>
Polynomials are <em>algebraic</em> expression which can be defined as a product of binomials:
(1)
Where:
- i-th root
- n - Grade
- a - Leading coefficient
<em>Quadratic</em> equations are polynomials of grade 2 and we can reduce (1) into this form and then rewritten to <em>standard</em> form:
p(x) = a · (x - r₁) · (x - r₂)
p(x) = a · x² - a · (r₁ + r₂) · x + a · r₁ · r₂
If we know that a = 3, r₁ = -5 and r₂ = -3, then the quadratic equation is:
p(x) = 3 · x² - 3 · [-5 + (-3)] · x + 3 · (-5) · (-3)
p(x) = 3 · x² + 24 · x + 15
By definition of polynomials, the polynomial 3 · x² + 24 · x + 15 represents a <em>quadratic</em> equation whose roots are - 5 and - 3 and whose <em>leading</em> coefficient is 3.
To learn more on quadratic equations: brainly.com/question/2263981
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