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
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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
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