Question

If $\alpha$ and $\beta$ are zeroes of the quadratic polynomial

$p\left(x\right)=x^2+7x+5$, then $(\alpha -\beta {)}^2$ equals:

• A. 69
• B. 9
• C. 49
• D. 29

Answer 1

The correct option is D 29

• Use the relationship between zeroes of polynomials and coefficients.

< Dictate and write:

𝛂 + 𝞫 = -b/a

𝛂 + 𝞫 = -7/1 = -7

𝛂𝞫 = c/a

𝛂𝞫 = 5/1 = 5 >

• Use the identity (a + b)2 to solve further.

< Dictate and write:

(𝛂 + 𝞫)2 = 𝛂2 + 𝞫2 + 2𝛂𝞫

Put the value of 𝛂 + 𝞫 = -7 and 𝛂𝞫 = 5

(-7)2 = 𝛂2 + 𝞫2 + 2(5)

49 = 𝛂2 + 𝞫2 + 10

𝛂2 + 𝞫2 = 49 - 10

𝛂2 + 𝞫2 = 39>.

• Use the identity (a - b)2.

< Dictate and write:

(𝛂 - 𝞫)2 = 𝛂2 + 𝞫2 - 2𝛂𝞫

Put the value 𝛂2 + 𝞫2 = 39 in above equation

(𝛂 - 𝞫)2 = 39 - 2(5)

(𝛂 - 𝞫)2 = 29>.