Question

(0) 6:5
(d) 2:1
. If a, ß are the roots of the equation 2x2 - 5x + 16 = 0 then
1/3 11/3
the value of
is
B
a α
BA
+
α​

Answer 1

Answer:

For the equation whose roots are 2α+3β,3α+2β,

The sum of the roots =2α+3β+3α+2β=5(α+β)→(I)

The product of the roots =(2α+3β)(3α+2β)

=6α

2

+13αβ+6β

2

=6(α

2

+β

2

)+13αβ

=6((α+β)

2

−2αβ)+13αβ

=6(α+β)

2

−12αβ+13αβ

=6(α+β)

2

+αβ →(II)

We also know α, β are the roots of the equation 2x

2

−5x−7=0

⇒α+β=5/2 →(III) and,

αβ=−7/2 →(IV)

Substituting (III),(IV) in (I),(II) for the equation to be found we get,

Sum of the roots =5×

2

5

=

2

25

Product of the roots=6×(5/2)

2

−7/2=

4

150

−

2

7

=

4

136

=

2

68

∴ the equation to be found is x

2

−(Sum of roots)x+Product of roots=0

⇒x

2

−(25/2)x+68/2=0

⇒2x

2

−25x+68=0