If - - are the roots of the equation ax 2- bx - c -0 such that -0- then the quadratic equation whose roots are - is given byA- - X 2- b - x - c -0B- ax 2- b - x - c -0C- - a - x 2- b - x - c -0D- a - x -2- b - x - c -0

The correct option is C |a| x^2 |b| x + |c| = 0 Sum of roots = |α| + |β| = α β (∵α lt; 0 and β lt; 0) = (α + β) = ( b/a ) = b/a = |b/a ...

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Byju's Answer

Standard XII

Mathematics

Relation between Roots and Coefficients for Quadratic

If α, β are t...

Question

If $α, β$ are the roots of the equation $a x^{2} + b x + c = 0$ such that $β < α < 0,$ then the quadratic equation whose roots are $| α |, | β |$ is given by

$| α | x^{2} + | b | x + | c | = 0$

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$a x^{2} - | b | x + c = 0$

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$| a | x^{2} - | b | x + | c | = 0$

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$a | x |^{2} + b | x | + c = 0$

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Solution

The correct option is C
$| a | x^{2} - | b | x + | c | = 0$

$S u m o f r o o t s = | α | + | β | = - α - β (∵ α < 0 a n d β < 0) = - (α + β) = - (- \frac{b}{a}) = \frac{b}{a} = ∣ ∣ \frac{b}{a} ∣ ∣ (∵ | α | + | β | > 0)$
and product of roots $= | α | | β | = | α β | = ∣ ∣ \frac{c}{a} ∣ ∣$
Hence, required equation is
$x^{2} - (∣ ∣ \frac{b}{a} ∣ ∣) x + ∣ ∣ \frac{c}{a} ∣ ∣ = 0 o r | a | x^{2} - | b | x + | c | = 0.$

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If α,β are the roots of the equation ax2+bx+c=0 such that β<α<0, then the quadratic equation whose roots are |α|,|β| is given by

The correct option is C |a|x2−|b|x+|c|=0 Sum of roots=|α|+|β|=−α−β (∵α<0 and β<0)=−(α+β)=−(−ba)=ba=∣∣ba∣∣(∵|α|+|β|>0) and product of roots =|α||β|=|αβ|=∣∣ca∣∣ Hence, required equation is x2−(∣∣ba∣∣)x+∣∣ca∣∣=0or |a|x2−|b|x+|c|=0.

If $α, β$ are the roots of the equation $a x^{2} + b x + c = 0$ such that $β < α < 0,$ then the quadratic equation whose roots are $| α |, | β |$ is given by