Question

one zero of polynomial 2x²-8x-m is 5/2. find the other zero and value of m

Answer 1

$p(x) = 2x {}^{2} - 8x - m$

If 5/2 is a zero of p(x).

•°•p(5/2)=0

$2 \times ( \frac{5}{2} ) { }^{2} - 8 \times \frac{5}{2} - m = 0 \\ 2 \times \frac{25}{4} - 8 \times \frac{5}{2} -m = 0 \\ \frac{25}{2} - 20 - m = 0 \\ \frac{25 - 40}{2} - m = 0 \\ - \frac{15}{2} - m = 0 \\ m = \frac{ - 15}{2}$

Answer 2

if x=5/2
2x^2-8x-m=0
2(5/2)^2-8(5/2)-m=0
25/2-20-m=0
-15/2-m=0
m=-15/2
2x^2-8x+15/2=0
4x^2-16x+15=0
4x^2-10x-6x+15
2x(2x-5)-3(2x-5)=0
(2x-3)(2x-5)=0
x=3/2    x=5/2
value of m=-15/2    other root is 3/2