Question

find a quadratic polynomial the sum of whose zeros is 7 and their product is 12 hence find the zeros of the polynomial

Answer 1

${x}^{2} - 7x + 12$
is the quadratic equation
x^2-sum of zeores.x+product of zeores
${x}^{2} - 4x - 3x + 12 \\ x(x - 4) - 3(x - 4) \\ (x - 3)(x - 4) \\ x = 3 \\ x = 4$
is your answer

Answer 2

if sum of zero is 7 and product of zero is 12

the formula for finding the quadratic polynomial is 

x²-{sum of zero}x+{product of zero}

x²-{7}x+12

x²-7x+12

hence to find its zero by splitting middle terms,
x²-7x+12=0
x²-4x-3x+12=0
x{x-4}-3{x-4}=0
{x-3}{x-4}=0

x-3=0      x-4=0
x=3          x=4

hence its two zero are 3 and 4