Question

Find the quadratic polynomial, sum of whose zeros is 8 and their products is 12. Hence, find the zeros of the polynomial ​

Answer 1

Step-by-step explanation:

See the Above solution

Answer 2

Step-by-step explanation:

Let α and β be the zeroes of the

required polynomial f(x).

Then (α+β) = 8 and αβ = 12

=>f(x) = x² – (α +β)x+ αβ

=>f(x) = x²- 8x + 12

Hence, required polynomial,

=>f(x) = x² – 8x + 12

=> f(x) = 0 => x²- 8х + 12= 0

=> x²-(6x + 2x) + 12 = 0

x²-6x 2x + 12 = 0

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

=> (x − 2)(x – 6) = 0

=> (x – 2) = 0 or (x – 6) =0

x = 2 or x = 6

So, the zeroes of f(x) are 2 and 6.

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