Question

if alpha and beta are the zeros and the quadratic polynomial FX = x square minus x minus 4 then the value of one upon alpha plus one upon beta minus alpha beta is ​

Answer 1

$\huge\star{\green{\mathfrak{\underline{AnSwEr}}}}$

$\large{\sf{\underline{\underline \blue{Step \: by \: step \: expanation:-}}}}$

•${\sf{\underline{\underline \red{Given-}}}}$

↠ $\sf\ A\: polynomial \: = \: x^2 \: - \: x \: - 4$

•${\sf{\underline{\underline \red{ To \: find -}}}}$

↠$\sf\frac{1}{\alpha} \: + \: \frac{1}{\beta}$

•$\large{\sf{\underline{\underline \red{Solution-}}}}$

From equation;

⇛$\sf\ a \: = \: 1, \: b \: = \: -1, \: c \: = -4$

Also;

⇛$\sf\ sum \: of \: roots(\alpha \: + \: \beta) \: = \frac{-b}{a}$

So;

↠$\sf\alpha \: + \beta \: = \: \frac{-(-1)}{1}$

↠$\sf\alpha \: + \beta \: = \: 1$

Again;

⇛$\sf\ product \: of \: roots(\alpha\beta) \: = \: \frac{c}{a}$

↠$\large\sf\alpha\beta \: = \: \frac{-4}{1}$

↠$\sf\alpha\beta \: = \: -4$

Now;

↠$\large\sf\frac{1}{\alpha} \: + \: \frac{1}{\beta} \: = \: \frac{\alpha \: + \: \beta}{\alpha\beta}$

According to it,consitute the values;

↠$\large\sf\frac{\alpha \: + \: \beta}{\alpha\beta} \: = \: \frac{1}{-4}$

Your final answer:

↠$\large\sf\frac{1}{\alpha} \: + \: \frac{1}{\beta} \: = \: \frac{1}{-4}$

Answer 2

Answer:

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