25) If α, β are the zereos of the quadratic polynomial x²-7x+10, find the value of α³+ β3

. By mid point theorem

. x²-5x-2x+10

. [x²-5x][-2x+10]

. x[x-5]-2[x+5]

. [x-2][x-5]

So,zeros of polynomial x²-7x+10 is

. x-2=0

X=2

.x-5=0

X=5

α β are 2 zeros

let α=2 β=5

so, α³-β3= 2³-5*3=8-15=7

@ Abhishek Vijayvergiya: Mid-point theorem is used in Geometry

Let f(x) = x² - 7x + 10

Here a = 1, b = -7 and c = 10

α + β = -b/a = -(-7)/1 = 7

αβ = c/a = 10/1 = 10

α³ + β³ = (α + β)³ - 3αβ(α + β)

Putting the respective values of α + β and αβ, we have

= (7)³ - 3(10)(7)

= 343 - 210

= 133

So, value of α³ + β³ = 133