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Question

Ifα andβ are the roots of the equationax2+bx+c=0, αβ=3 anda,bandc are in AP, thenα+β is equal to


A

-4

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B

1

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C

4

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D

-2

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Solution

The correct option is D

-2


Explanation for correct option:

Step 1: Apply the A.P relation between three given numbersa,bandc.

We have given a quadratic equationax2+bx+c=0, whose roots areα andβ, αβ=3and a,bandc are in A.P.

We have to find the value ofα+β.

Asa,bandc are in A.P.

2b=a+c

Step 2: Find the relationshipaandc.

and we haveαβ=3

αβ=ca3a=c

Step 3: Find the relationshipaandb.

so, above first equation.

2b=a+3a2b=4ab=2a

Step 4: Finding the value of the sum of roots.

α+β=-baα+β=-2aa=-2α+β=-2

Hence, the correct option is(D).


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