Find all zeroes of the polynomial 2x^4+7x^3-19x^2-14x+30 if two of its zeroes are root 2, - root 2.
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Given : 2x⁴+7x³-19x²-14x+30
two of its zeroes are root 2, - root 2.
To Find : all zeroes of the polynomial
Solution:
two of its zeroes are root 2, - root 2.
Hence ( x - √2) (x - (-√2)) = x² - 2 is a factor
2x⁴+7x³-19x²-14x+30 = (x² - 2) ( 2x² + 7x - 15)
2x² + 7x - 15 = 2x² + 10x - 3x - 15
= 2x(x + 5) - 3(x + 5)
= (2x - 3)(x + 5)
Hence other zeroes are
3/2 , - 5
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