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Question

Ruhi and Tara were asked to solve a quadratic equation ax2+bx+c=0,a0.Ruhimadesomemistakeinwritingbandfoundtherootsas3and-\dfrac {1}{2}.Tara,too,mademistakeinwritingcandfoundtheroots-1and-\dfrac {1}{4}$. Find the correct roots of the given equation

A
2,34
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B
3,1
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C
12,1
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D
3,14
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Solution

The correct option is A 2,34
Ruhi makes mistake in b value of a and c are correct

product of roots =c/a=3/2 is correct

Tara makes mistake in 'c' values of 'a' and 'b' are correct

sum of roots =b/a=5/4 is correct

Let roots be m,n

m+n=5/4 and mn=3/2

m+32m==5/4

4m2+5m6=0

(4m3)(m+2)=0

m=2 or m=3/4

n=3/4 or n=2

roots are 2,34

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