Question

1
16.
176
α
find the value of k.
18. If a and B are the zeroes of the quadratic polynomial f(x) = 4x2 - 5x - 1, then find the value of
(i)a-B
(ii)a? +BP33 (iii)a^ + Bº
(iv)aß? + a’ß -5
1
1
1 1
(v) - +
(vi) + aß (vii) (viii)a+B
α β
B р
α β
B В
1
α β
1
(ix) +
(xi) - + +2
+3aß
β α
B В
B р
1 1
B?
(xii)a^ß +a pº (xiii) - 2aB (xiv)-
В
a?
B?
(x) a²
+
a
+
a
α
a
+
a
22
2.​

Answer 1

Answer:

α and β are zero of the polynomial:

p(x)=4x2-5x-1

a=4,b=-5,c=-1

So, Sum of the zeroes = α + β=-\(\frac ba\) \(= \frac{5}{4}\)

Product of the zeroes = αβ=\(\frac ca\) \(= \frac{{ - 1}}{4}\)

Now, α2β + αβ2 = αβ(α + β)

\(= \frac{5}{4}\left( {\frac{{ - 1}}{4}} \right)\)

\(= \frac{{ - 5}}{{16}}\).