Question

if alpha and beta are the zeros of the quadratic polynomial f of x is equal to x squared minus x minus 4 find the value of one by Alpha Plus One by beta minus alpha beta

Answer 1

Hey mate

Here is ur answer,

$f(x) = {x}^{2} - x - 4$
Roots of the quadratic equation is alpha and beta.

Sum of the roots:

$= > \: \alpha + \beta = \frac{ - b}{a}$
$= > \: \frac{ - ( - 1)}{1}$

=> 1.

Product of zeroes:

$= > \: \alpha \beta = \frac{c}{a}$

=> -4/1

=> -4.

From the question,

$= > \: \frac{1}{ \alpha } + \frac{1}{ \beta } - \alpha \beta$

$= > \: \frac{ \alpha + \beta }{ \alpha \beta } - \alpha \beta$

$= > \: \frac{1}{ - 4} - ( - 4)$

$= > \: \frac{ - 1}{4} + 4$


$= > \: \frac{15}{4}$

:-)Hope it helps u. 《《 VIDYA》》》

Answer 2

The value is $\bf \frac{1}{ \alpha } + \frac{1}{ \beta } - \alpha \beta = \frac{ 15}{4}$.

Given:

• A quadratic polynomial.
• $f(x)= {x}^{2} - x - 4$

To find:

• Find the value of $\frac{1}{ \alpha } + \frac{1}{ \beta } - \alpha \beta$

Solution:

A standard quadratic polynomial $\bf f(x) = a {x}^{2} + bx + c$, a≠0, have two zeros

l$\alpha \: and \: \beta$

then

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

and

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

Step 1:

Find the value of $\alpha + \beta \: and \: \alpha \beta$

From the above written relationship of zeros and coefficients of expression.

$\alpha + \beta = - \frac{ - 1}{1}$

$\alpha + \beta = 1 \: \: \: ...eq1$

and

$\alpha \beta = \frac{ - 4}{1}$

$\alpha \beta = - 4 \: \: ...eq2$

Step 2:

Find the value of $\frac{1}{ \alpha } + \frac{1}{ \beta }$

we can manipulate the expression,

As shown

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

put the values from eq1 and eq2

$\frac{1}{ \alpha } + \frac{1}{ \beta } = \frac{ - 1}{4} \: \: ...eq3$

Step 3:

Find the value of expression.

Put the values from eq3 and eq2.

$\frac{1}{ \alpha } + \frac{1}{ \beta } - \alpha \beta = \frac{ - 1}{4} - ( - 4)$

$\frac{1}{ \alpha } + \frac{1}{ \beta } - \alpha \beta = \frac{ - 1}{4} + 4$

$\frac{1}{ \alpha } + \frac{1}{ \beta } - \alpha \beta = \frac{ - 1 + 16}{4}$

$\frac{1}{ \alpha } + \frac{1}{ \beta } - \alpha \beta = \frac{ 15}{4}$

Thus,

The value is

$\bf \frac{1}{ \alpha } + \frac{1}{ \beta } - \alpha \beta = \frac{ 15}{4}$

Learn more:

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2)If alpha and beta are the root of quadratic equation 2 x square minus x minus 1 is equal to zero find alpha and beta

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