Question

if Alfa n beata are the zero of quadratic polynomial 2x^2+5x+kfind the value of k such that (Alfa+bita)^2-alfa×bita=24​

Answer 1

Zeroes are @ (alpha) and ß (beta)

Quadratic polynomial = 2x^2 + 5x + k

Where,

a = 2

b = 5

c = k

We know,

Sum of zeroes ( @ + ß ) = - b/a = -5/2

Product of zeroes ( @ß) = c/a = k / 2

Now,

Squaring both sides -:

( @ + ß ) ^2 = (-5/2)^2

@^2 + 2@ß + ß^2 = 25/4

@^2 + @ß + @ß + ß^2 = 25/4

@^2 + ß^2 + @ß + @ß = 25/4

Given,

@^2 + ß^2 + @ß = 21/4

So,

21/4 + k/2 = 25/4

k/2 = 25 / 4 - 21/4

k/2 = 25 - 21/4

k/2 = 4/4

k/2 = 1

k = 2 × 1

k = 2

Value of k = 2

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Hope it helps...!!!