The polynomial (x2 – bx + 8) and (x2 – 11x + 3a) is divisible by (

1.	The polynomial (x2 – bx + 8) and (x2 – 11x + 3a) is divisible by (x + 5) then which of the following statement is/are correct regarding a and b?Statement 1: Product of a and b is negativeStatement 2: Both a and b are in fraction1. Only 12. Only 23. Both 1 and 24. Neither 1 nor 2
Answer» Correct Answer - Option 2 : Only 2 Given: The given polynomials are (x² – bx + 8) and (x² – 11x + 3a) are divisible by (x + 5) Concept Used: According to factor theorem If (x - a) is factor of P(x) then P(a) = 0 Calculation: Let the polynomials are P(x) = (x² – bx + 8) and G(x) = (x² – 11x + 3a). If (x + 5) is the factor of polynomials. Then according to the factor theorem ∴ P(-5) = 0 Now, put x = -5 in P(x) So, 33 + 10b = 0 ⇒ b = -33/10 And also G(-5) = 0 Now, put x = -5 in G(x) So, 80 + 3a = 0 ⇒ a = -80/3 So, product of both is positive and both the value is in fraction Hence, option (2) is correct

The polynomial (x2 – bx + 8) and (x2 – 11x + 3a) is divisible by (x + 5) then which of the following statement is/are correct regarding a and b?Statement 1: Product of a and b is negativeStatement 2: Both a and b are in fraction1. Only 12. Only 23. Both 1 and 24. Neither 1 nor 2

Answer» Correct Answer - Option 2 : Only 2

Given:

The given polynomials are (x² – bx + 8) and (x² – 11x + 3a) are divisible by (x + 5)

Concept Used:

According to factor theorem If (x - a) is factor of P(x) then P(a) = 0

Calculation:

Let the polynomials are P(x) = (x² – bx + 8) and G(x) = (x² – 11x + 3a). If (x + 5) is the factor of polynomials. Then according to the factor theorem

∴ P(-5) = 0

Now, put x = -5 in P(x)

So, 33 + 10b = 0

⇒ b = -33/10

And also G(-5) = 0

Now, put x = -5 in G(x)

So, 80 + 3a = 0

⇒ a = -80/3

So, product of both is positive and both the value is in fraction

Hence, option (2) is correct

Discussion

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