Answer:
The zeroes are -1 and 13
Positive value: [tex]x = 13[/tex]
Step-by-step explanation:
Given
[tex]2x^2 - 24x = 26[/tex]
Solving (a): The zeros
[tex]2x^2 - 24x = 26[/tex]
Subtract 26 from both sides
[tex]2x^2 - 24x - 26= 26-26[/tex]
[tex]2x^2 - 24x - 26= 0[/tex]
Divide through by 2
[tex]\frac{1}{2}(2x^2 - 24x - 26) = \frac{1}{2} * 0[/tex]
[tex]x^2 - 12x - 13 = 0[/tex]
Expand
[tex]x^2 - 13x + x - 13 = 0[/tex]
Factorize:
[tex]x(x-13)+1(x-13)=0[/tex]
[tex](x+1)(x-13)=0[/tex]
Split:
[tex]x +1 =0\ or\ x-13=0[/tex]
[tex]x =-1\ or\ x=13[/tex]
Hence, the zeroes are -1 and 13
Solving (b): The positive value of x
In (a) above:
[tex]x =-1\ or\ x=13[/tex]
The positive value is:
[tex]x = 13[/tex]
