Question

If a b c are in ap then the roots of the equation ax^2+bx+c =0 has

Answer 1

HERE IS UR ANSWER DEAR,

a,b,c are in AP,then

second term -first term = third term -second term

t2 - t1 = t3 - t2

here,

• t1 = a
• t2 = b
• t3 = c

so,

b-a = c-b

2b. = a+c

b = a+c/2

given equation is

ax² +bx +c= 0

$let \: \alpha and \: \beta \: be \: the \: roots \: of \\ \: the \: equation$

$sum \: of \: the \: roots \: = \alpha + \beta = \frac{ - b}{a}$

$\: \: \: \: \: \: \: \: \: \: \alpha + \beta = \frac{ - (a + c)}{2a}$

$\: \: \: \: \: \: \: \: \: \ \alpha + \beta = \frac{ - a - c}{2a}$

$\: \: \: \: \: \alpha + \beta = ( \frac{ - a}{2a} ) \: + \: ( \frac{ - c}{2a} )$

by comparing LHS and RHS,

$\alpha = \frac{ - a}{2a} : \beta = \frac{ - c}{2a}$

$product \: of \: the \: roots \: = \alpha \beta = \frac{c}{a}$

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