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प्रश्न
If the roots of ax2 + bx + c = 0 are in the ratio m : n, then:
पर्याय
mn a2 = (m + n) c2
mn b2 = (m + n) ac
mn b2 = (m + n)2 ac
mn b2 = (m – n)2 ac
MCQ
उत्तर
mn b2 = (m + n)2 ac
Explanation:
We have `α/β = "m"/"n"`
⇒ `α/"m" = β/"n"` ⇒ `(α + β)/("m" + "n") = sqrt((αβ)/("mn"))` by ratio proportion
∴ mn(α + β)2 = αβ(m + n)2
⇒ `"mn" ((-"b")/"a")^2 = ("m" + "n")^2 "c"/"a"`
∴ mn b2 = (m + n)2 ac
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