Answer:
The equation is [tex]8x^2 -6x+1=0[/tex]
Step-by-step explanation:
We need to find the quadratic equation which is in the form:
[tex]ax^2 + bx + c = 0[/tex]
We are given sum S = 3/4 and Product P = 1/8
The quadratic equation in terms of sum and products can be written as:
[tex]x^2 - Sx + P =0[/tex]
Where S is sum and P is product. Putting their values we get:
[tex]x^2-\frac{3}{4}x+\frac{1}{8}=0[/tex]
The co-efficient should be integer so, taking LCM of 4 and 8
[tex]\frac{8x^2 -6x+1}{8} =0\\Dividing\,\,both\,\,sides\,\,by\,\,8\\8x^2 -6x+1=0[/tex]
So,
Co-efficient are: a = 8 , b = -6 and c= 1
Solving the equation:
[tex]8x^2 -6x+1=0\\8x^2 -2x -4x+1=0\\8x(x-1/4)-4(x-1/4) =0\\(x-1/4)(8x-4)=0\\x-1/4 =0\,\, and\,\, 8x-4 =0\\x = 1/4\,\, and x \,\,= 4/8 = 1/2[/tex]
So values of x are 1/4 and 1/2
Sum: 1/4+1/2 = 1+2/4 = 3/4
Product: 1/4 * 1/2 = 1/8
