Question

if one roots of the equation 3x²+ax-4=0 is 1, then the other root is:​

Answer 1

Answer:

Other root is -4/3

Explanation:

Given equation,

⇒ 3x² + ax - 4 = 0

Whose one of the roots is 1.

We need to find the other root.

Let's find ‘a’ first,

By substituting x = 1

⇒ 3(1)² + a(1) - 4 = 0

⇒ 3 + a - 4 = 0

⇒ - 1 + a = 0

⇒ a = 1

∴ a = 1

Now the equation is :-

⇒ 3x² + ax - 4

⇒ 3x² + 1(x) - 4

⇒ 3x² + x - 4

We know,

Product of roots :- Constant term/Coefficient of x

Then,

Product of roots :- -4/3

⇒ one root × other root = -4/3

We have, one root as 1

So,

⇒ 1 × other root = -4/3

⇒ other root = -4/3 ÷ 1

⇒ other root = -4/3

∴ The other root is -4/3

_______________________

Let us check :-

Substituting x as 4/3 in the equation must give us zero.

⇒ 3x² + x - 4

⇒ 3(-4/3)² + (-4/3) - 4

⇒ 3(16/9) - 4/3 - 4

⇒ 16/3 - 4/3 - 4

⇒ 12/3 - 4

⇒ 4 - 4

⇒ 0

Hence, proved !!