Hey there!
Solutions:
Let the polynomial be ;
p(x) = ax² + bx + c,
i ) According to question,
Sum of zeroes = 1/4
or, - b / a = 1 / 4
Let a = 1;
- b / 1 = 1/4
b = -1/4
And,
Product of zeroes = -1
or, c / a = -1
c / 1 = -1
or, c = -1.
The required polynomial is :
= ax² + bx + c
Putting values of a , b ,c;
= x² + (-1/4)x + (-1)
= x² - 1/4 x - 1
ii) Sum of zeroes = √2
or, - b / a = √2
let a = 1;
-b / 1 = √2
b = - √2
product of zeroes = 1 / 3
or, c / a = 1/3
c / 1 = 1/3
c = 1/3
The required polynomial is:
ax² + bx + c
Putting values of a , b , c;
= x² + (-√2)x + 1/3
Taking 3 common,
= 3 { x² - √2x + 1/3)
= 3x² - 3√2x + 1
iii) Sum of zeroes = 0
or, - b/a = 0
b = 0.
Product of zeroes = √5
or, c / a = √5
c /1 = √5
c = √5
Putting values of a,b,c;
x² + 0x + √5
= x² + √5
iv) Sum of zeroes = 1
or, - b/a = 1
- b / 1 = 1
b = -1
Product of zeroes = 1
or, c / a = 1
c = 1.
putting values of a,b,c;
x² + (-1)x + 1
= x² - x + 1
v) Sum of zeroes = -1/4
or , -b/a = - 1/4
-b / 1 = -1 / 4
b = 1/4
Product of zeroes = 1 / 4
or, c / a = 1/4
Let a=1;
c = 1/4.
x² + 1/4x + 1/4
Taking 4 common,
= 4 (x² + 1/4x + 1/4)
= 4x² + x + 1
vi) Sum of zeroes = 4
or, -b/a = 4
b = -4.
product of zeroes = 1
or, c/a = 1
= x² + (-4)x + 1
= x² - 4x +1
Hope It helps You!
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Answers & Comments
..Heya mate..I have done 2 que. for you remaining u can do on yourself.
Hey there!
Solutions:
Let the polynomial be ;
p(x) = ax² + bx + c,
i ) According to question,
Sum of zeroes = 1/4
or, - b / a = 1 / 4
Let a = 1;
- b / 1 = 1/4
b = -1/4
And,
Product of zeroes = -1
or, c / a = -1
Let a = 1;
c / 1 = -1
or, c = -1.
The required polynomial is :
= ax² + bx + c
Putting values of a , b ,c;
= x² + (-1/4)x + (-1)
= x² - 1/4 x - 1
ii) Sum of zeroes = √2
or, - b / a = √2
let a = 1;
-b / 1 = √2
b = - √2
And,
product of zeroes = 1 / 3
or, c / a = 1/3
Let a = 1;
c / 1 = 1/3
c = 1/3
The required polynomial is:
ax² + bx + c
Putting values of a , b , c;
= x² + (-√2)x + 1/3
Taking 3 common,
= 3 { x² - √2x + 1/3)
= 3x² - 3√2x + 1
iii) Sum of zeroes = 0
or, - b/a = 0
let a = 1;
b = 0.
And,
Product of zeroes = √5
or, c / a = √5
Let a = 1;
c /1 = √5
c = √5
The required polynomial is:
ax² + bx + c
Putting values of a,b,c;
x² + 0x + √5
= x² + √5
iv) Sum of zeroes = 1
or, - b/a = 1
Let a = 1;
- b / 1 = 1
b = -1
And,
Product of zeroes = 1
or, c / a = 1
Let a = 1;
c = 1.
The required polynomial is:
ax² + bx + c
putting values of a,b,c;
x² + (-1)x + 1
= x² - x + 1
v) Sum of zeroes = -1/4
or , -b/a = - 1/4
Let a = 1;
-b / 1 = -1 / 4
b = 1/4
And,
Product of zeroes = 1 / 4
or, c / a = 1/4
Let a=1;
c = 1/4.
The required polynomial is:
ax² + bx + c
Putting values of a,b,c;
x² + 1/4x + 1/4
Taking 4 common,
= 4 (x² + 1/4x + 1/4)
= 4x² + x + 1
vi) Sum of zeroes = 4
or, -b/a = 4
Let a = 1;
b = -4.
And,
product of zeroes = 1
or, c/a = 1
Let a = 1;
c = 1.
The required polynomial is:
ax² + bx + c
Putting values of a,b,c;
= x² + (-4)x + 1
= x² - 4x +1
Hope It helps You!