Question

Ruhi and Tara were asked to solve a quadratic equation $a{x}^2+bx+c=0,a\ne 0$$.Ruhimadesomemistakeinwritingbandfoundtherootsas$3$and$-\dfrac {1}{2}$.Tara,too,mademistakeinwritingcandfoundtheroots$-1$and$-\dfrac {1}{4}$. Find the correct roots of the given equation

• A. $-2,\frac{3}{4}$
• B. $3,-1$
• C. $-\frac{1}{2},-1$
• D. $3,-\frac{1}{4}$

Answer 1

The correct option is A $-2,\frac{3}{4}$

Ruhi makes mistake in $b$ $\Rightarrow$ value of $a$ and $c$ are correct

$\Rightarrow$product of roots =$c/a=-3/2$ is correct

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

$\Rightarrow$ sum of roots =$-b/a=-5/4$ is correct

Let roots be $m,n$

$\Rightarrow m+n=-5/4$ and $mn=-3/2$

$\Rightarrow m+\frac{-3}{2m}==-5/4$

$\Rightarrow 4m^2+5m-6=0$

$\Rightarrow (4m-3)(m+2)=0$

$\Rightarrow m=-2$ or $m=3/4$

$\Rightarrow n=3/4$ or $n=-2$

$\therefore$ roots are $-2,\frac{3}{4}$