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Explanation:
Answer :
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m = -24
Step-by-step explanation :
α and β are the roots of x² + 5x + m = 0
x² coefficient = 1
x coefficient = 5
constant term = m
RELATIONSHIP BETWEEN ZEROES AND COEFFICIENTS :
⇒ Sum of zeroes = -(x coefficient)/x² coefficient
α + β = -5/1
α + β = -5
⇒ Product of zeroes = (constant term)/x² coefficient
α × β = m/1
αβ = m
2α + 5β = -1
2α + 2β + 3β = -1
2(α + β) + 3β = -1
2(-5) + 3β = -1
-10 + 3β = -1
3β = 10 - 1
3β = 9
β = 9/3
β = 3
⇒ α + β = -5
α + 3 = -5
α = -5 - 3
α = -8
We got, αβ = m
m = α × β
m = (-8) × 3
m = -24
∴ The value of m is -24