Question

If alpha and beta are the zeroes of the polynomial 2y ^2 + 7y + 5, then write the [2]
value of alpha + beta + alpha beta

Answer 1

Here's your solution.

Answer 2

Question :-

If alpha and beta are the zeroes of the polynomial 2y² + 7y + 5, then write the [2] value of α + β + αβ

Answer :-

The value is α + β + αβ is -1

Solution :-

Let's factorize the quadratic polynomial 2y² + 7y + 5 first,

$\sf\longrightarrow 2 {y}^{2} + 7y + 5$

$\sf\longrightarrow 2 {y}^{2} + (5 + 2)y + 5$

$\sf\longrightarrow 2 {y}^{2} + 5y + 2y + 5$

$\sf\longrightarrow y (2y + 5) + 1 (2y + 5)$

$\sf\longrightarrow (y + 1) (2y + 5)$

$\sf\therefore Either, \: (y + 1) = 0 \: or, \: (2y + 5) = 0$

$\sf\rightarrow y + 1 = 0$

$\sf\rightarrow y = -1$

Or,

$\sf\rightarrow 2y + 5 = 0$

$\sf\rightarrow 2y = -5$

$\sf\rightarrow y = \dfrac{-5}{2}$

Hence, the zero of the polynomials are - 1 and -5/2

Now, Let α be -1 and β be -5/2

Putting the values,

$\sf\longrightarrow \alpha + \beta + \alpha \beta$

$\sf\longrightarrow - 1 + \dfrac{-5}{2} + (-1) \times \dfrac{-5}{2}$

$\sf\longrightarrow - 1 - \dfrac{5}{2} + \dfrac{5}{2}$

$\sf\huge\therefore - 1$