Question

if alpha and beta are the zeros of quadratic polynomial ax2+BX+C THEN EVALUATE 1UPON ALPHA+1UPON BETA

Answer 1

given

p(x)= ax²+bx+x

we know that,

sum of zeroes= -b/a (coefficient of x/ coefficient of x²)

$\alpha + \beta = \frac{ - b}{a}$
also,

Product of zeroes= c/a (constant term/ coefficient of x²)

$\alpha \beta = \frac{c}{a}$
now,

$\frac{1}{ \alpha } + \frac{1}{ \beta } \\ \\ = \frac{ \beta + \alpha }{ \alpha \beta } \\ \\ on \: substituting \: the \: values \\ \\ = \frac{ - b}{a} \div \frac{c}{a} \\ \\ = \frac{ - b}{a} \times \frac{a}{c} \\ \\ = \frac{ - b}{c}$
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