Question

find all the zeros of the polynomial 2x4-10x3+5x2+15x-12 two of its zeroes are root3/2 and -root3/2

Answer 1

Therefore the  zeroes of the polynomial are:

$\sqrt{ \frac{3}{2} } , - \sqrt{ \frac{3}{2} } , 1, 4$


Hope it helps!

Answer 2

$\bf{hey}$
$\underline{here \: is \: the \: answer}$
since two zeros are √3/2 and -√3/2

hence

⏩ x=√3/2 and x=-√3/2

⏩ (x-√3/2) (x+3/2) ✓✓

⏩x²-√3/2²

⏩x²-3/2

⏩ 2x²-3

p(x)= 2x⁴-10x³+5x²+15x-12

divide 2x²-3 with p(x)

division refers to the pic..✓✓

then the quotant will be

x²-5x+4

factorize it

⏩x²-4x-x+4

⏩x(x-4)-1(x-4)

⏩(x-4)(x-1)

hence zeroes are

x-4=0

x=4

and

x-1=0

x=1

hence zeroes are

√3/2 , -√3/2,4and 1

$\underline{hope \: it \: helps}$

$\boxed{thanks}$