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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p(x) = x^2-(sum of zeroes)x+(product of zeroes)
=x^2-√2-3/2
=2x^2-2√2x-3 (After taking LCM)
Sum = √2
Product = -3/2
(Difference)^2= (sum)^2-4(product)
Difference=√8=2√2
a+b=√2
a-b=2√2
=2a=3√2
= a=3√2/2
And b = √2-a
=√2-3√2/2
(2√2-3√2)/2
=-√2/2
=x^2-√2-3/2
=2x^2-2√2x-3 (After taking LCM)
Sum = √2
Product = -3/2
(Difference)^2= (sum)^2-4(product)
Difference=√8=2√2
a+b=√2
a-b=2√2
=2a=3√2
= a=3√2/2
And b = √2-a
=√2-3√2/2
(2√2-3√2)/2
=-√2/2
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