Question

If alpha, beta are the zeros of the polynomial 2x^2-4x+b, find b if 2alpha +3beta=8

Answer 1

Heya

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Alfa + Beta = 2

And

Alfa × Beta = b/2

ACCORDING TO THE QUESTION

2( Alfa + Beta ) + Beta = 8

=>

2 ( 2 ) + Beta = 8

=>

Beta = 4 And Alfa = -2

=>

Alfa × Beta = b/2

=>

4 × -2 = b/2

=>

b = -16

Answer 2

Answer:

The value of $b$ is $-16$.

Step-by-step explanation:

It is given that the polynomial is $2x^{2} -4x+b=0$

The roots are alpha and beta.

Sum of roots is $\alpha +\beta= -\frac{-4}{2} =2$ ---(1)

Product of roots $\alpha \beta =\frac{b}{2}$

According to question,

we are given that $2\alpha +3\beta =8$ ---(2)

It can be written as $2\alpha +2\beta +\beta =8$

$2(\alpha +\beta )+\beta =8$

Using (1)

$2(2)+\beta =8$

$\beta =8-4$

$\beta =4$

Using it in (2)

$2\alpha =8-3(4)$

$\alpha =-2$

Using values in product of roots

$-2*4=\frac{b}{2}$

$b=-16$

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