Question

Help me please I will mark as brainlist ​

Answer 1

Answer:

$\frac{ \alpha + \beta + \gamma }{ - d}$

Step-by-step explanation:

If we simplify that fraction, we get

$\frac{ \alpha + \beta + \gamma }{ \alpha \beta \gamma }$

Keep that in mind.

If y, a ,b are zeroes of the cubic polynomial, then that means

$(x - \alpha )(x - \beta )(x - \gamma )$

make up the polynomial.

Notice that leading xoeffeicent will be 1, so the roots will multiply to

$- d$

so

$\alpha \beta \gamma = - d$

which gives us

$\frac{ \alpha + \beta + \gamma }{ - d}$

Proof:

Consider the function

$(x - 2)(x - 3)(x - 5)$

The roots are 2, 3, 5.

D is -30 so we get

Using the value,

$\frac{2 + 3 + 5}{ 30} = \frac{1}{3}$

If we use the orginal equation, we get

$\frac{1}{6} + \frac{1}{10} + \frac{1}{15} = \frac{10}{30} = \frac{1}{3}$