what are the sum and product of zeros of polynomial 4√5x² - 24x - 9√5
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Step-by-step explanation:
It is given that 2+3,2−3 are two zeroes of the polynomial f(x)=2x4−9x3+5x2+3x−1
∴(x−(2+3))(x−(2−3))=(x−2−3)(x−2+3)
=(x−2)2−(3)2
=x2−4x+4−3
=x2−4x+1
∴(x−(2+3))(x−(2−3))=x2−4x+1 is a factor of f(x)
Now divide f(x) by x2−4x+1
∴f(x)=(x2−4x+1)(2x2−x−1)
Hence, the other two zeroes of f(x) are the zeroes of the polynomial 2x2−x−1
2x2−x−1=(2x+1)(x−1)
Hence, the other two zeroes are −21,1.
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