Question

if alpha and beta are the zeroes of the quadratic polynomial f(x) = 4x²-5x-1,then find the value of 1/alpha+ 1/beta - alpha beta​

Answer 1

Answer:

-19/4

Step-by-step explanation:

Given a quadratic polynomial such that,

$f(x) = 4 {x}^{2} - 5x - 1$

Also, the zereos are alpha and beta.

To find the value of

1/alpha + 1/beta - alpha beta

We know that,

Sum of roots = -b/a

$= > \alpha + \beta = - \frac{( -5 )}{4} \\ \\ = > \alpha + \beta = \frac{5}{4}$

Product of roots = c/a

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

Now, finding the value of,

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

We will get,

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

Substituting the values, we get,

$= \dfrac{ \frac{5}{4} }{ - \frac{1}{4} } - ( - \dfrac{1}{4} ) \\ \\ = - 5 + \frac{1}{4} \\ \\ = \frac{ - 20 + 1}{4} \\ \\ = - \frac{19}{4}$

Hence, the required value is -19/4.