Question

If alpha and beta are the zeros of the quadratic polynomial p x = x^2 + kx + 45 such that (Alpha - beta)^2 = 144 , find the value of K

Answer 1

Given quadratic polynomial is p(x) = x2 + kx + 45
Recall that sum of roots of ax2 + bx + c is (−b/a)
Hence (α + β) = − (k/1) = − k
Given (α + β)2 = 144
⇒ (- k)2 = 144
⇒ k2 = 144
⇒ k = √144 = ± 12

Answer 2

Answer:

Step-by-step explanation:

Let α and β be two zeros then ,

α + β = -k              [ -b/a] ……………………… [2]

αβ = 45            [ c/a]  ……………..[1]

Given that ,

{ α – β} ^ 2  = 144

α ^2 + β ^2 - 2 αβ = 144

α ^2 + β ^2 – 2 x 45 = 144       [using 1]  

α ^2 + β ^2 – 90 = 144

α ^2 + β ^2 = 144 + 90

α ^2 + β ^2 = 234

Now ,

[α + β]^2 - 2αβ = 234

[α + β]^2 – 2 x 45 = 234           [using 1]

[α + β]^2  = 234 + 90

[α + β]^2  = 324

[α + β] =  ± 18

Hence,  

-k =  ± 18                                 [using 2]