Question

1. Find all zeroes of the polynomial
$(2x^{4} - {9x}^{3} + {5x}^{2} + 3x - 1)$
if two of its zeroes are
$(2 + \sqrt{3} )and(2 - \sqrt{3} )$
2. If A(-2, 1), B(a, 0), C(4, b) and D(1, 2) are the vertices of a parallelogram abcd, find the value of a and b. hence find the lengths of its sides.​

Answer 1

as same as this bas aapko zeroes change krni hain

Answer 2

Here is your answer:

1)let p(x)=2x^4-9x^3+5x^2+3x-1

(2-{3}) is an zero of p(x)

Then x-(2-{3})is a factor of p(x)

=x-2+{3}is a factor

Similarly,(2+{3}) is a zero of p(x)

Then (x-(2+{3})is a factor of p(x)

=x-2-{3} is a factor

Divisor=(x-2-{3})(x-2+{3})

=x^2-4x+1

Divide p(x) by g(x)

2x^4-9x^3+5x^2+3x-1/x^2-4x+1

=2x^2-x-1

Let p(x)=2x^2-x-1

By using splitting middle term

=2x^2-x-1=0

=2x^2-2x+x-1=0

=2x(x-1)+1(x-1)=0

=(2x+1)=0 or (x-1)=0

=2x=-1. Or x=1

=x=-1/2

Therefore zeroes are 2+{3},2-{3},-1/2 and 1