Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively ^5,2
Answers
Answer:
Using the quadratic equation formula,
x
2
−(Sum of root)x+(Product of root)=0
Substitute the value in the formula, we get
x
2
−
4
1
x−1=0
4x
2
−x−4=0
(ii)
2
,
3
1
Using the quadratic equation formula,
x
2
−(Sum of root)x+(Product of root)=0
Substitute the value in the formula, we get
x
2
−
2
x+
3
1
=0
Multiply by 3 to remove denominator,
3x
2
−3
2
x+1=0
(iii) 0,
5
Using the quadratic equation formula,
x
2
−(Sum of root)x+(Product of root)=0
Substitute the value in the formula, we get
x
2
−0x+
5
=0
x
2
+
5
=0
(iv) 1, 1
Using the quadratic equation formula,
x
2
−(Sum of root)x+(Product of root)=0
Substitute the value in the formula, we get
x
2
−1x+1=0
x
2
−x+1=0
(v)
4
−1
,
4
1
Using the quadratic equation formula,
x
2
−(Sum of root)x+(Product of root)=0
Substitute the value in the formula, we get
x
2
−
4
−1
x+
4
1
=0
Multiply by 4
4x
2
+x+1=0
(vi) 4, 1
Using the quadratic equation formula,
x
2
−(Sum of root)x+(Product of root)=0
Substitute the value in the formula, we get
x
2
−4x+1=0
Answer:
(i)1/4, -1 Now formula of quadratic equation is x²-(Sum of root)x + (Product of root)
= 0 Plug the value in formula we get x² –(1/4)x -1
= 0 Multiply by 4 to remove denominator we get 4x² - x -4 = 0
(ii) √2 , 1/3 Now formula of quadratic equation is x²-(Sum of root)x + (Product of root)
= 0 Plug the value in formula we get x² –(√2)x + 1/3
= 0 Multiply by 3 to remove denominator we get 3x² - 3√2 x + 1 = 0
(iii) 0, √5 Now formula of quadratic equation is x²-(Sum of root)x + (Product of root)
= 0 Plug the value in formula we get x² –(0)x + √5 = 0 simplify it we get x² + √5 = 0
(iv) 1,1 Now formula of quadratic equation is x²-(Sum of root)x + (Product of root)
= 0 Plug the value in formula we get x² –(1)x + 1 = 0 simplify it we get x² - x + 1 = 0
(v) -1/4 ,1/4 Now formula of quadratic equation is x²-(Sum of root)x + (Product of root) = 0 Plug the value in formula we get x² –(-1/4)x + 1/4 = 0 multiply by 4 we get 4x² + x + 1 = 0
(vi) 4,1 Now formula of quadratic equation is x²-(Sum of root)x + (Product of root)
= 0 Plug the value in formula we get x² –(4)x + 1 = 0 x2 –4x + 1 = 0