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Question

If α and β are the roots of the equation a x2 + bx + c. find the equation whose roots are - α and - β.


A

ax2 + bx + c = 0

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B

ax2 - bx + c = 0

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C

cx2 + bx + a = 0

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D

cx2 - bx + a = 0

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Solution

The correct option is B

ax2 - bx + c = 0


Solution: ax2 + bx + c roots are α and β

α + β = ba

α . β = ca

When roots are -α and -β

-α -β = -(α + β) = ba

(-α) × (-β) = αβ = ca

Equation is x2 - (-α - β) × + (-α) (-β) = 0

x2 - (+ ca)n + ca = 0

ax2 - bx + c = 0

Alternatively

If roots are equal in magnitude but opposite in sign we can replace x by (-x) in the given equation.

a(x)2 + b(-x) + c = 0

ax2 - bx + c = 0


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