Question

if alpha,beta are the roots of the equation 2x^2-6x+a=0 and 2alpha+5beta=12​

Answer 1

Answer:

Given

$\alpha + \beta = - \frac{ - 6}{2} = 3........(i)$

$2 \alpha + 5 \beta = 12.........(ii)$

Apply (ii) – (i)×2, we get

$3 \beta = 6$

$\beta = 2$

from (i),

$\alpha = 3 - \beta = 3 - 2 = 1$

so,

$\alpha \beta = 2 \times 1 = 2$

a/q,

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

i.e

$\frac{a}{2} = 2$

$a = 2 \times 2 = 4$

so value of a = 4.

Ans.

Answer 2

Given

\alpha + \beta = - \frac{ - 6}{2} = 3........(i)α+β=−

2

−6

=3........(i)

2 \alpha + 5 \beta = 12.........(ii)2α+5β=12.........(ii)

Apply (ii) – (i)×2, we get

3 \beta = 63β=6

\beta = 2β=2

from (i),

\alpha = 3 - \beta = 3 - 2 = 1α=3−β=3−2=1

so,

\alpha \beta = 2 \times 1 = 2αβ=2×1=2

a/q,

\alpha \beta = \frac{a}{2}αβ=

2

a

i.e

\frac{a}{2} = 2

2

a

=2

a = 2 \times 2 = 4a=2×2=4

so value of a = 4.