Question

Ifα,β are the zeros of the polynomial 2x2+7x+5 then find the value of α+β+αβ.

Answer 1

Answer:

-1

Step-by-step explanation:

α and β are the zeros of polynomial 2x2 + 7x + 5

α + β = Sum of zeros = -(coefficient of x)/(coefficient of x2) = -7/2

αβ = Product of zeros = (constant term)/(coefficient of x2) = 5/2

α + β + αβ = (α + β) + αβ

= -7/2 + 5/2  

= -2/2

= -1

Answer 2

The given question is If α and β are the zeros of the polynomial 2x2+7x+5 then find the value of α+β+αβ.

The given expression is

$2 {x}^{2} + 7x + 5$

we have to find the value of

$\alpha + \beta + \alpha \beta$

In general, a polynomial is an expression that contains intermediate, exponents, constants and terms.

The sum of zeroes of the equation is given as

$\alpha + \beta$

The product of zeroes is given as

$\alpha \beta$

The formula to find the sum and product of the equations is

$\alpha + \beta = \frac{ - coefficient \: of \: x \: }{co \: efficient \: of \: {x}^{2} }$

$\alpha \beta = \frac{constant \: term}{co \: efficient \: of \: {x}^{2} }$

The sum and product of the zeroes of the equation

$2 {x}^{2} + 7x + 5$

is obtained as

$\alpha + \beta = \frac{ - 7}{2}$

$\alpha \beta = \frac{5}{2}$

substituting the above values in the question, we get the answers as

$\alpha + \beta + \alpha \beta = \frac{ - 7}{2} + \frac{5}{2} = \frac{ - 7 + 5}{2}$

$\frac{ - 2}{2} = - 1$

Therefore, the value is obtained as

$\alpha + \beta + \alpha \beta = - 1$

Hence, the final answer to the given question is -1.

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