Question

if alpha and beta are zeros of polynomial 3 x square - 8 x + 4 find one by Alpha Plus One by beta ​

Answer 1

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Answer 2

The value of the expression $\frac{1}{\alpha }+ \frac{1}{\beta}$  is  2.

Given,

α and β are the zeros of the polynomial $3x^{2} -8x+4.$

To Find,

We have to find the value of the expression  $\frac{1}{\alpha }+ \frac{1}{\beta} .$

Solution,

The method of finding the value of the expression  $\frac{1}{\alpha }+ \frac{1}{\beta}$  is as follows –

We know that for a quadratic equation $ax^{2} +bx+c=0$, the formula of the sum of its roots is  $-\frac{b}{a}$ and the formula of the product of the roots is $\frac{c}{a}$.

Let for the quadratic equation $3x^{2} -8x+4=0$, $a=3, b=-8,c=4$.

The sum of the roots of the quadratic equation is

$\alpha +\beta =-\frac{b}{a}=\frac{-(-8)}{3}=\frac{8}{3}$ .    

Also, the product of the roots of the quadratic equation is $\alpha \beta =\frac{c}{a}=\frac{4}{3}$ .

Now, $\frac{1}{\alpha }+ \frac{1}{\beta} = \frac{\alpha +\beta }{\alpha \beta }$

$=\frac{\frac{8}{3} }{\frac{4}{3}}=\frac{8}{3} *\frac{3}{4}$

$=2$ .

Hence, the value of the expression $\frac{1}{\alpha }+ \frac{1}{\beta}$  is  2.

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