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If a and B are the zeros of x² + 5x + 8 = 0, then what is the value of (a + b)? |
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Answer» p(x) = x² + 5x + 8α 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/aProduct of roots = x₁x₂ = (constant TERM)/(coefficient of x²) = c/aOn comparing p(x) = x² + 5x + 8 with the standard form, that is, ax² + bx + c, we get,a = 1b = 5c = 8So,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/aαβ + βγ + γα = c/aαβγ = -d/a |
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