If p - q - r - R -and p - q - r are in A-P with non zero common difference- then the roots of px 2-2 qx - r -0 areA- rational and equalB- real and distinctC- imaginaryD- real and equal

The correct option is B real and distinctp,q,r are in A.P. ⇒ 2q=p+r px^2+2qx+r=0 D=4q^2 4pr =(p+r)^2 4pr =(p r)^2 gt;0 (∵Common difference is non ze ...

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Standard XII

Mathematics

Sum of n Terms

If p , q , r ...

Question

If $p, q, r \in R^{+}$ and $p, q, r$ are in A.P with non zero common difference, then the roots of $p x^{2} + 2 q x + r = 0$ are

rational and equal

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imaginary

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real and equal

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real and distinct

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Solution

The correct option is D real and distinct
$p, q, r$ are in A.P.
$\Rightarrow 2 q = p + r$
$p x^{2} + 2 q x + r = 0 D = 4 q^{2} - 4 p r = (p + r)^{2} - 4 p r = (p - r)^{2} > 0 (∵ Common difference is non zero)$

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If p,q,r∈R+ and p,q,r are in A.P with non zero common difference, then the roots of px2+2qx+r=0 are

The correct option is D real and distinctp,q,r are in A.P. ⇒2q=p+r px2+2qx+r=0D=4q2−4pr =(p+r)2−4pr =(p−r)2>0 (∵Common difference is non zero)

If $p, q, r \in R^{+}$ and $p, q, r$ are in A.P with non zero common difference, then the roots of $p x^{2} + 2 q x + r = 0$ are

The correct option is D real and distinct
$p, q, r$ are in A.P.
$\Rightarrow 2 q = p + r$
$p x^{2} + 2 q x + r = 0 D = 4 q^{2} - 4 p r = (p + r)^{2} - 4 p r = (p - r)^{2} > 0 (∵ Common difference is non zero)$