Question

a for which one root of the quadratic equation (a? – 5a + 3) x2 + (30 - 1)
O is twice as large as the other.
JAIEEE 2003]
14. If o. Bare the roots of the equation ax? - bx + b = 0, prove that
Vo Va Va
the equation x2 + ax + b = 0 has equal roots,
IB
16 Ь
= 0.​

Answer 1

Answer:

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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

Answer 2

Answer:

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