Question

Hello
please solve this one ....

Answer 1

Answer:

17

Step-by-step explanation:

Given Equation is x² + 7x + 12.

Here, a = 1, b = 7, c = 12.

Given that α,β are roots of the equation.

(i) Sum of roots:

α + β = -b/a

α + β = -7.

(ii) Product of roots:

⇒ αβ = c/a

⇒ αβ = 12

Now,

α + β + 2αβ

= -7 + 2(12)

= -7 + 24

= 17

Hope it helps!

Answer 2

HOLA

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Given , P(x) =
$x {}^{2} \: + \: 7x \: + \: 12 \\ \\ x {}^{2} \: + \: 4x \: + \: 3x \: + \: 12 \\ \\ x \: (x + 4) \: + \: 3(x + 4) \\ \\ (x + 4) \: + \: (x + 3) \\ \\ x \: = \: - \: 4 \: \: \\ \\ x \: = \: 3 \\ \\ \\ so \: \ \: \: \: \: \alpha \: = \: - 4 \: \: \: \: \: \: \: \beta \: = \: 3 \\ \\ \\ ( \alpha + \beta ) \: = \: - 4 \: + 3 \: = \: - 7 \\ \\ ( \alpha \beta ) \: = \: 12 \\ \\ ( \: \alpha \: + \: \beta \:) \: + \: 2( \alpha \beta ) \\ \\ - 7 \: + \: 2( 12) \: = \: 17$
The second method which easier than this is given in the image

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HOPE U UNDERSTAND ❤❤❤