Question

if the polynomial 2x^2-5x+k has two zeros a and b then a^2+b^3+ab=21/4 then find the value of k​

Answer 1

Answer:

The value of k is 2

Step-by-step explanation:

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