Question

Write quadratic polynomial with the given numbers as sum and Product of its Zeroes respectively 1)1/4. 2)0,✓5

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Answer 1

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+