Form a quadratic polynomial whose zeroes are (i) 5 and -8 (ii) 2±√3
Answers
Question
Form a quadratic polynomial whose zeroes are (i) 5 and -8 (ii) 2±√3
Step by step explanation
(i)5 and -8
The Quadratic Equation whose zeros are 5 and -8 is
f(x)= x² -(sum of zeros)x +ab
f(x)= x² -(5-8)x +5×(-8)
f(x)= x² -(-3)x -40
f(x)= x² +3x-40
The Quadratic equation whose zeroes are 5 and -8 is x²+3x-40.
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(ii) 2 and ±√3
The Quadratic Equation whose zeros are 2 +√3 and 2 -√3 is
f(x)= x² -(sum of zeros)x +ab
f(x)= x²-(2+√3+2-√3)x+(2+√3)(2-√3)
f(x)= x² -(2 +2 )x +(2²-(√3)²)
f(x)= x² -4x +(4-3)
f(x)= x² -4x +1
- The Quadratic equation whose zeroes are 2 +√3 and 2 -√3 is x² -4x +1.
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Answer:
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Step-by-step explanation:
( i ) 5 and -8
The Quadratic Equation whose zeros are 5 and -8 is
f(x)= x² -(sum of zeros)x +ab
f(x)= x² -(5-8)x +5×(-8)
f(x)= x² -(-3)x -40
f(x)= x² +3x-40
The Quadratic equation whose zeroes are 5 and -8 is x²+3x-40.
(ii) 2 and ±√3
The Quadratic Equation whose zeros are 2 +√3 and 2 -√3 is
f(x)= x² -(sum of zeros)x +ab
f(x)= x²-(2+√3+2-√3)x+(2+√3)(2-√3)
f(x)= x² -(2 +2 )x +(2²-(√3)²)
f(x)= x² -4x +(4-3)
f(x)= x² -4x +1
- The Quadratic equation whose zeroes are 2 +√3 and 2 -√3 is x² -4x +1.