Question

Find the zeroes of the polynomial 2x4+7x3-19x2-14x+30 ,if two of its zeroes are root2 and.Minus root 2

Answer 1

Let p(x) = 2x^4 +7x^3 - 19x^2 -14x +30

Given zeroes = √2 nd -√2

Sum of zeroes (s) = √2 + (-√2)

√2-√2

0

Product of zeroes(p) = (√2)(-√2)

-2

W.K.T,... k(x^2 -sx +p)

therefore, x^2 -0x + (-2)

... x^2 -2

Since( x^2 -2 ) is formed from the zeroes of p(x), .. it must be the factor of p(x)

By dividing from p(x) ...we get

2x^2 + 7x -15

2x^2 +10x -3x -15

2x(x+5) -3(x+5)

(2x-3)(x+5)

x= 3/2 ,..x= -5

Hence , zeroes of p(x) are √2,-√2, 3/2, -5