Question

Write the quadratic equation whose roots are −5 and −3, and whose leading coefficient is 3.

Answer 1

By definition of polynomials, the polynomial 3 · x² + 24 · x + 15 represents a quadratic equation whose roots are - 5 and - 3 and whose leading coefficient is 3.

How to derive a quadratic equation based on given roots

Polynomials are algebraic expression which can be defined as a product of binomials:

$p(x) = a \cdot \prod \limits_{i=1}^{n} (x - r_{i})$     (1)

Where:

• $r_{i}$ - i-th root
• n - Grade
• a - Leading coefficient

Quadratic equations are polynomials of grade 2 and we can reduce (1) into this form and then rewritten to standard 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 quadratic equation whose roots are - 5 and - 3 and whose leading coefficient is 3.

To learn more on quadratic equations: https://brainly.com/question/2263981

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