If the roots of the equation a2+bx+c = 0 are of the formk+1k and k+2k+1, then a+b+c2 is equal to

# If the roots of the equation a2+bx+c = 0 are of the form, then ${\left(a+b+c\right)}^{2}$ is equal to

1. A

b2-4ac

2. B

b2-2ac

3. C

2b2-ac

4. D

${\mathrm{\Sigma a}}^{2}$

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### Solution:

we have.$\frac{\mathrm{k}+1}{\mathrm{k}}+\frac{\mathrm{k}+2}{\mathrm{k}+1}=-\frac{\mathrm{b}}{\mathrm{a}}..................\left(\mathrm{i}\right)$
and $\frac{\mathrm{k}+1}{\mathrm{k}}\cdot \frac{\mathrm{k}+2}{\mathrm{k}+1}=\frac{\mathrm{c}}{\mathrm{a}}$……………………….(ii)
From Eq. (i),
$1+\frac{1}{\mathrm{k}}+1+\frac{1}{\mathrm{k}+1}=-\frac{\mathrm{b}}{\mathrm{a}}$
…………………..(iii)
From Eq. (ii),

Now, on substituting the value of kin Eq. (iii), we get
$2+\frac{\mathrm{c}-\mathrm{a}}{2\mathrm{a}}+\frac{1}{\frac{2\mathrm{a}}{\mathrm{c}-\mathrm{a}}+1}=-\frac{\mathrm{b}}{\mathrm{a}}$

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