Correct Answer - Option 2 : -10
Given:
The polynomial = 6x2 - 7x + a
The polynomial is divisible by (6x + 5)
Concept used:
If (ax + b) is a factor of polynomial P(x) then p(-b/a) = 0
Calculation:
Here, P(x) = 6x2 - 7x + a
Here (6x + 5) is a factor fo P(x)
So, P(-5/6) = 0
⇒ 6(-5/6)2 - 7(-5/6) + a = 0
⇒ 6(25/36) + (35/6) + a = 0
⇒ (25/6) + (35/6) + a = 0
Multing both the sides by 6 we get,
⇒ 25 + 35 + 6a = 0
⇒ 60 + 6a = 0
⇒ 6a = -60
⇒ a = -10
∴ The value of a is -10.