Find a quadratic polynomial each with the given numbers as the sum and product of it's zeroes respectively
1/4 ,-1
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(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+5
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