Question

If a and B are the zeros of x² + 5x + 8 = 0, then what is the value of (a + b)?​

Answer 1

Given:-

• p(x) = x² + 5x + 8
• α and β are the roots of p(x)

To find:-

• The value of (α + β)

Answer:-

We know that, for a polynomial ax² + bx + c, having roots x₁ and x₂,

• Sum of roots = x₁ + x₂ = - (coefficient of x)/(coefficient of x²) = -b/a
• Product of roots = x₁x₂ = (constant term)/(coefficient of x²) = c/a

On comparing p(x) = x² + 5x + 8 with the standard form, that is, ax² + bx + c, we get,

• a = 1
• b = 5
• c = 8

So,

sum of roots = -b/a

→ α + β = -5/1

→ α + β = -5 Ans.

Extra knowledge:-

For a cubic polynomial ax³ + bx² + cx + d, having roots α, β and γ,

• α + β + γ = -b/a
• αβ + βγ + γα = c/a
• αβγ = -d/a