Question

The value of 'a' for which one root of the quadratic
equation (a? – 5a +3)x2 – (3a – 1)x + 2 = 0 is
twice as large as other is​

Answer 1

Step-by-step explanation:

a

2

−5a+3)x

2

+(3a−1)x+2=0

Let the roots be α

1

β, given β=2α

⇒3α=

(a

2

−5a+3)

−(3a−1)

…(1) (Sum of roots)

⇒2α

2

=

a

2

−5a+3

2

…(2) (Product of roots)

⇒

(a

2

−5a+3)

2

(3a−1)

2

=

a

2

−5a+3

9

⇒

(a

2

−5a+3)

2

(3a−1)

2

−9(a

2

−5a+3)

=0

⇒9a

2

−6a+1−9a

2

+45a−27=0

⇒39a−26=0

⇒a=

3

2