if the zeros of the polynomial p(x) = x2 + kx + 12 differ by unity, find the value - Maths - Polynomials

Question

if the zeros of the polynomial p(x) = x2 + kx + 12 differ by
unity, find the value

Manbar Singh · Accepted Answer

Dear student,
Assuming your question is;
If the zeros of the polynomial p(x) = x2 + kx + 12
differ by unity, find the value

Let px = x2 + kx + 12 ,  be the given polynomial
Let α and β are zeroes of px
Now, α - β = 1     given    
1Comparing the given polynomial with standard polynomial ax2 + bx + c, we get,a = 1  ;  b = k   , c = 12now,α + β = - ba = - k⇒α + β = - k      
2adding 1 and 2, we get2α = 1 - k⇒α = 1 - k2 from 1, we getβ = α - 1 = 1 - k2 - 1 = -k + 12

now,α × β = ca = 12⇒1-k2 × -1 + k2 = 12⇒1 - k1 + k = - 48⇒1 - k2 = -48⇒k2 = 49⇒ k = ±7

if the zeros of the polynomial p(x) = x2 + kx + 12 differ by unity, find the value.