Write quadratic polynomial with the given numbers as sum and Product of its Zeroes respectively 1)1/4. 2)0,✓5
Answers
Answer:
Product of zeros =αβ=2×3=6. Thus when α=2 and β=3 the sum and product of zero's are 5 and 6. Thus we can split the 2nd term of a quadratic polynomial x2−5x+6=0.
Step-by-step explanation:
Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.
(i) 41, −1 (ii) 2,31 (iii) 0,5
(iv) 1,1 (v) 4−1,41 (vi) 4,1
Answer
(i) 41, -1
Using the quadratic equation formula,
x2−(Sum of root)x+(Product of root)=0
Substitute the value in the formula, we get
x2−41x−1=0
4x2−x−4=0
(ii) 2,31
Using the quadratic equation formula,
x2−(Sum of root)x+(Product of root)=0
Substitute the value in the formula, we get
x2−2x+31=0
Multiply by 3 to remove denominator,
3x2−32x+1=0
(iii) 0, 5
Using the quadratic equation formula,
x2−(Sum of root)x+(Product of root)=0
Substitute the value in the formula, we get
x2−0x+5=0
x2+