Question
Download Solution PDFIf the roots of equation ax2 + bx + c = 0 are equal and have opposite signs, then which one of the following statements is correct?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
If α and β are the two roots of the quadratic equation Ax2 + Bx + C = 0, then α + β = \(\rm -\dfrac{B}{A}\) and αβ = \(\rm \dfrac{C}{A}\).
Calculation:
Let's say that α and β are the two roots of the quadratic equation ax2 + bx + c = 0, then α + β = \(\rm -\dfrac{b}{a}\) and αβ = \(\rm \dfrac{c}{a}\).
It is given that α = -β.
∴ -β + β = \(\rm -\dfrac{b}{a}\)
⇒ \(\rm -\dfrac{b}{a}\) = 0
⇒ b = 0.
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