Question

write down the relations between the roots and coefficients of the equation 3x^2-x+1=0​

Answer 1

Step-by-step explanation:

3x

2

+ax−2=0

Since, one root is 1, then x=1

⇒ 3(1)

2

+a(1)−2=0

⇒ 3+a−2=0

⇒ a+1=0

⇒ a=−1

⇒ Now, it is given that ax

2

+6ax−b=0 has equal roots.

∴ b

2

−4ac=0

⇒ (6a)

2

−4(a)(−b)=0

⇒ 36a

2

+4ab=0

⇒ 36(−1)

2

+4(−1)b=0 [ Substituting a=−1 ]

⇒ 36−4b=0

⇒ 4b=36

∴ b=9

Answer 2

Step-by-step explanation:

$\huge \pink{ \boxed{\bf \blue{Answer}}}$

Correct option is A)

3x

2

+ax−2=0

Since, one root is 1, then x=1

⇒ 3(1)

2

+a(1)−2=0

⇒ 3+a−2=0

⇒ a+1=0

⇒ a=−1

⇒ Now, it is given that ax

2

+6ax−b=0 has equal roots.

∴ b

2

−4ac=0

⇒ (6a)

2

−4(a)(−b)=0

⇒ 36a

2

+4ab=0

⇒ 36(−1)

2

+4(−1)b=0 [ Substituting a=−1 ]

⇒ 36−4b=0

⇒ 4b=36

∴ b=9