What according to helen are the disadvantages in going to college ?
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Helen said that she was a child when she first read Shakespeare. She was most impressed by Macbeth. Later, she read many of Shakespeare’s plays and was so captivated that she even remembered some parts of his plays by heart. She was completely in love with Shakespeare. Sometimes she enjoyed his little songs and sometimes his sonnets. She shared that she did not understand many things in Shakespeare but still liked his writings the most.
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Explanation:
f(x) = kx³ – 8x² + 5
Roots are α – β , α & α +β
Sum of roots = – (-8)/k
Sum of roots = α – β + α + α +β = 3α
= 3α = 8/k
= k = 8/3α
or we can solve as below
f(x) = (x – (α – β)(x – α)(x – (α +β))
= (x – α)(x² – x(α+β + α – β) + (α² – β²))
= (x – α)(x² – 2xα + (α² – β²))
= x³ – 2x²α + x(α² – β²) – αx² +2α²x – α³ + αβ²
= x³ – 3αx² + x(3α² – β²) + αβ² – α³
= kx³ – 3αkx² + xk(3α² – β²) + k(αβ² – α³)
comparing with
kx³ – 8x² + 5
k(3α² – β²) = 0 => 3α² = β²
k(αβ² – α³) = 5
=k(3α³ – α³) = 5
= k2α³ = 5
3αk = 8 => k = 8/3α
(8/3α)2α³ = 5
=> α² = 15/16
=> α = √15 / 4
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