If - and - are the roots of the equation x 2-6 x -1-0- then what is - equal to-A- 6 - - 3 -2D- 4 -2

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Quadratic Equations

If α and β ar...

Question

If $α a n d β$ are the roots of the equation $x^{2} + 6 x + 1 = 0,$ then what is $| α - β |$ equal to?

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3 \sqrt{2}

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4 \sqrt{2}

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\frac{3}{2}

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Solution

The correct option is C $4 \sqrt{2}$
$∵ α a n d β$ are the roots of the equation $x^{2} + 6 x + 1 = 0 ∴ α + β = - 6 a n d α β = 1 N o w, (α - β)^{2} = (α + β)^{2} - 4 α β = (- 6)^{2} - 4 = 36 - 4 = 32 \Rightarrow | α - β | = \sqrt{32} = 4 \sqrt{2}$

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If α and β are the roots of the equation x2+6x+1=0, then what is |α−β| equal to?

The correct option is C 4√2∵α and β are the roots of the equation x2+6x+1=0∴α+β=−6 and αβ=1Now,(α−β)2=(α+β)2−4αβ=(−6)2−4=36−4=32⇒|α−β|=√32=4√2

If $α a n d β$ are the roots of the equation $x^{2} + 6 x + 1 = 0,$ then what is $| α - β |$ equal to?

The correct option is C $4 \sqrt{2}$
$∵ α a n d β$ are the roots of the equation $x^{2} + 6 x + 1 = 0 ∴ α + β = - 6 a n d α β = 1 N o w, (α - β)^{2} = (α + β)^{2} - 4 α β = (- 6)^{2} - 4 = 36 - 4 = 32 \Rightarrow | α - β | = \sqrt{32} = 4 \sqrt{2}$