Find a quadratic polynomial, the sum and product of whose zeroes are √2 and -3/2
respectively. Also, find its zeroes.
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Answer:
2x^2 - 2✓2x - 3 = 0
Zeroes are (3✓2)/2 and -✓2/2
Step-by-step explanation:
Let the zeroes be a & b
Sum of the zeroes is given as a + b
Product of the zeroes is given as a*b
The equation using a+b and a*b is given as
x^2 - (a+b)x - ab = 0
=> x^2 - ✓2x - 3/2 = 0
=> 2x^2 - 2✓2x - 3 = 0
Zeroes are obtained by solving the equation
i.e. (3✓2)/2 and -✓2/2
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