given that 2xsquared-5x+k is a perfect square . find the value of k

Answer 1

2x^2 - 5x + k
What we can do here is to get the discriminant. For a quadratic equation with form ax^2 + bx + c = 0, the discriminant is equal to
b^2 - 4ac
The value of discriminant for a perfect square (which therefore has equal or double roots) is equal to zero. Substituting,
b^2 - 4ac = 0
(-5)^2 - 4(2)(k) = 0
25 - 8k = 0
-8k = -25
k = 25/8

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