Question

find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients x square - 12 x + 32
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Answer 1

Step-by-step explanation:

Zeroes are 4 and 8.

Step-by-step explanation :

f(x) = x² - 12x + 32

By Middle Term Factorisation

→ f(x) = x² - 8x - 4x + 32

→ f(x) = x(x - 8) - 4(x - 8)

→ f(x) = (x - 4)(x - 8)

To find zeroes, f(x) = 0, then

→ 0 = (x - 4)(x - 8)

By Zero Product Rule

→ x - 4 = 0 and x - 8 = 0

→ x = 4 and x = 8

Let α and β be the zeroes of the polynomial.

So, α = 4 and β = 8

Verification :

On comparing the given polynomial with ax² + bx + c, we get

a = 1, b = - 12, c = 32

Sum of Zeroes :

→ α + β = 4 + 8 = 12

Also, - b/a = - (- 12)/1 = 12

Product of Zeroes :

→ αβ = (4)(8) = 32

Also, c/a = 32/1 = 32

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