Question

Find the quadratic polynomial the sum of whose zeros is 8 and their product is 12

Answer 1

GIVEN

Sum of zeroes = 8

The product of zeroes = 12

TO FIND

The Quadratic Polynomial

SOLUTION

To form a Quadratic Polynomial. we should follow the following rule,

P(x) = K[ x^2 - (Sum of zeroes)x + Product of zeroes]

So lets substitute the given Values;

k[ x^2 - 8x + 12]

= x^2 - 8x + 12 [ k = 1]

VERIFICATION

x^2 - 8x + 12 = 0

=> x^2 - 6x - 2x + 12 = 0

=> x(x-6) - 2(x - 6) = 0

=> (x - 6)(x - 2) = 0

x = 6 or x = 2

Now sum of zeroes= 6 + 2 = 8

Product of zeroes = 6 × 2 = 12

Hence Our Answer is Correct !