Question

find the zero of the polynomial f(x)=x^2-25x+144​

Answer 1

Answer:

Given quadratic polynomial f(x) = x2+px+45 Let α and β be the roots(zeros) of the given quadratic polynomial f(x) = x2+px+45 Also, given (α - β)2 = 144 We know that, (α - β)2 = (α + β)2 - 4αβ Now, we have from the quadratic polynomial f(x) = x2+px+45, (α + β) = -p, αβ = 45 ⇒144 = (-p)2 - 4(45) ⇒144 = p2 - 180 ⇒144 + 180 = p2 ⇒324 = p2 ⇒p2 = 324 ⇒p = 18