Question

27.If the sum and the product of the zeroes of a polynomial are 0 and 1 then find the
polynomial
28 Find the 31st term of AP whose 11th term is 38 and the 16th term is 73.​

Answer 1

(1)

$let \: \alpha \: \: and \: \: \beta \: be \: the \: \: zeroes \: of \: the \: polynomial \\ \\ \alpha + \beta = 0 \\ \alpha \times \beta = 1 \\ \\ then \: the \: formula \: tofind \: the \: quadratic \: equation \: is \: \\ x ^{2} - (sum \: of \: zeros \: )x \: + product \: ofzeros \: = 0 \\ x ^{2} - 0x + 1 = 0 \\ x ^{2} + 1 = 0$

Hence the quadratic equation is x^2 +1 =0

(2)

Given

tn = a + (n-1 )d

11th term is 38

t11 = a + ( 11-1 )d ____(1)

16th term is 73

t16 = a +(16-1) d ____(2)

Solving 1 and 2

a + 10d -38 =0

a+ 15d- 73 =0

(-) (-) (+)

_______

-5d +35 =0

- 5d = -35

- d = -35/5

d = 7

sub d = 7 in a +10 d=38

a + 10 (7) = 38

a +70 =38

a = -32

Hence a =-32 and d =7

31st term = t31

tn = a +(n -1 )d

t31 = -32 + (31 -1)7

t31 = -32 +30 ×7

t31 = -32 +210

t31 = 178.

Hope this helps you.