My Learning Cart
?
Categories
Account

If the polynomial g(x) = x^2 + bx + c has roots -2 and 3, what is the value of b

₹0.0
Login to Download
  • 📥 Instant PDF Download
  • ♾ Lifetime Access
  • 🛡 Secure & Original Content

What’s inside this PDF?

Question: If the polynomial g(x) = x^2 + bx + c has roots -2 and 3, what is the value of b?

Options:

  1. 1
  2. -1
  3. 5
  4. -5

Correct Answer: 5

Solution: 

Using Vieta\'s formulas, the sum of the roots (-2 + 3) = 1, which means b = -1.

If the polynomial g(x) = x^2 + bx + c has roots -2 and 3, what is the value of b

Practice Questions

Q1
If the polynomial g(x) = x^2 + bx + c has roots -2 and 3, what is the value of b?
  1. 1
  2. -1
  3. 5
  4. -5

Questions & Step-by-Step Solutions

If the polynomial g(x) = x^2 + bx + c has roots -2 and 3, what is the value of b?
  • Step 1: Identify the roots of the polynomial g(x). The roots given are -2 and 3.
  • Step 2: Use Vieta's formulas, which state that for a polynomial of the form g(x) = x^2 + bx + c, the sum of the roots is equal to -b.
  • Step 3: Calculate the sum of the roots: -2 + 3 = 1.
  • Step 4: Set the sum of the roots equal to -b: 1 = -b.
  • Step 5: Solve for b by multiplying both sides by -1: b = -1.
  • Vieta's Formulas – Vieta's formulas relate the coefficients of a polynomial to sums and products of its roots.
  • Roots of a Polynomial – Understanding how to find the coefficients of a polynomial given its roots.
Soulshift Feedback ×

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?

Not likely Very likely
Home Practice Performance eBooks