Find a quadratic polynomial, the sum and product of whose zeroes are root2 and -3/2. Also find its zeroes.
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=k(x²-(α+β)x+αβ)
=k(x²-√2x+(-3/2))
=k[(2x²-2√2x-3)/2]
here k=2
the polynomial is 2x²-2√2x-3
=2x²+√2x - 3√2x - 3
=√2x(√2x+1)-3(√2x+1)
=(√2x-3)(√2x+1)
⇒√2x-3=0 or ⇒√2x+1=0
⇒x=3/√2 or ⇒x= - 1/√2
=k(x²-√2x+(-3/2))
=k[(2x²-2√2x-3)/2]
here k=2
the polynomial is 2x²-2√2x-3
=2x²+√2x - 3√2x - 3
=√2x(√2x+1)-3(√2x+1)
=(√2x-3)(√2x+1)
⇒√2x-3=0 or ⇒√2x+1=0
⇒x=3/√2 or ⇒x= - 1/√2
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