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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Quadratic Equation

NTA Abhyas 2020 · Mathematics · Quadratic Equation

If the roots of the equation ax ^ 2 + bx + c = 0 are in the ratio...

If the roots of the equation ax2+bx+c=0{ax}^{2} + bx + c = 0 are in the ratio m:nm: n , then

Options

  1. Amnb^{2} = ac{\left(m + n\right)}^{2}
  2. Bb2(m+n)=mnb^{2}\left(m + n\right) = mn
  3. Cm+n=b2mnm + n = b^{2}mn
  4. D{mnc}^{2} = ab{\left(m + n\right)}^{2}

Correct answer

A. mnb^{2} = ac{\left(m + n\right)}^{2}

Step-by-step solution

Let the roots are mrmr and nrnr

mr+nr=−ba⇒r(m+n)=−ba…(1)mr + nr = \dfrac{- b}{a} ⇒ r \left(m + n\right) = \dfrac{- b}{a} \ldots \left(1\right)

and mnr2=ca…(2)mnr^{2} = \dfrac{c}{a} \ldots\left(2\right)

Eliminating rr , we get

b2mn=ca(m+n)2b^{2}mn = ca{\left(m + n\right)}^{2}
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