If a root of the equations x2-p x-q-0 and x2- x-0 is common- then its value will be where p - and q - A- q-pB- p - q-q-C- q-p or p - q-q-D- None of these

The correct option is C Let the common root be y, then y^2 + py + q =0 and y^2 + nbsp;αy+β=0 On solving by cross multiplication, we have y^2/pβ qα = y/q β=1 ...

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Standard XI

Mathematics

Geometric Progression

If a root of ...

Question

If a root of the equations $x^{2} + p x + q = 0$ and $x^{2} + α x + β = 0$ is common, then its value will be ( where p ≠ α and q ≠ β )

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None of these

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Solution

The correct option is C

Let the common root be y, then $y^{2} + p y + q = 0$ and $y^{2} + α y + β = 0$

On solving by cross multiplication, we have

$\frac{y^{2}}{p β - q α} = \frac{y}{q - β} = \frac{1}{α - p}$

∴ $y = \frac{q - β}{α - p} a n d \frac{y^{2}}{y} = y = \frac{p β - q α}{q - β}$

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If a root of the equations x2+px+q=0 and x2+αx+β=0 is common, then its value will be ( where p ≠ α and q ≠ β )

The correct option is C Let the common root be y, then y2+py+q=0 and y2+αy+β=0 On solving by cross multiplication, we have y2pβ−qα=yq−β=1α−p ∴ y=q−βα−pandy2y=y=pβ−qαq−β

If a root of the equations $x^{2} + p x + q = 0$ and $x^{2} + α x + β = 0$ is common, then its value will be ( where p ≠ α and q ≠ β )