For which value of k will the roots of the equation 2x^2-5x+k=0 be real and rational numbers

1 answer:

5 0

The trick here is to find the discriminant, b^2-4ac, of the equation 2x^2 - 5x + k.
Here a=2, b=-5, and c=k.

So long as the discriminant is 0 or greater than 0, your roots will be real and rational numbers.

Thus, compute b^2-4ac: (-5)^2 - 4(2)(k)

Let this equal zero and solve for k: 25=8k; k=25/8.

So long as k is 25/8 or smaller, b^2-4ac will be 0 or greater, and the roots will be real and rational.

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We have that
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A (0,2) B(2,4) C(0,0)

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using a graph tool
see the attached figure

therefore

Line 1 Segment AC equals 2. Segment FE equals 2. Segment AC is congruent to segment FE
so
Segment AC equals 2-------> is correct
Segment FE equals 2-----> is correct
Segment AC is congruent to segment FE------> is correct

Line 2 ∠A ≅ ∠F------> is correct

Line 3 Length of segment AB. A (0, 2) B (2, 4) d equals square root of quantity x sub 2 minus x sub 1 squared plus quantity y sub 2 minus y sub 1 squared, d equals square root of quantity 0 minus 2 all squared plus quantity 2 minus 4 all squared, d equals square root of negative 2 squared plus negative 2 squared, d equals square root of 4 plus 4, d equals square root of 8 segment AB = 2.83

find the distance AB
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AB=2.83
so
Line 3 is correct

Line 4 Length of segment DE. D (2, 0) E (4, 4) d equals square root of quantity x sub 2 minus x sub 1 squared plus quantity y sub 2 minus y sub squared, d equals square root of quantity 2 minus 4 all squared plus quantity 0 minus 4 all squared, d equals square root of negative 2 squared plus negative 4 squared, d equals square root of 4 plus 16, then d equals square root of 20 segment DE = 4.47

find the distance DE
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DE=4.47
so
Line 4------> is correct

Line 5 segment AB is congruent with segment DE
AB is not congruent with DE
so
Line 5 is not correct

therefore

the answer is
the student make the first mistake in line 5

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