Question

find the zeroes of a quadratic polynomial verify the relative between the zeroes and it's coefficients
$x^{2} - 7x + 10$
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Answer 1

Let the zeroes of the polynomial be α and β.

• Zeroes of the polynomial x² – 7x + 10

→ x² – 7x + 10

→ x² – (5+2)x + 10

→ x² - 5x - 2x + 10

→ x(x - 5) –2(x - 5)

→ x – 2 , x – 5

→ x = 2,5

• α = 2, β = 5

As We know that the different relations b/w the zeroes of the polynomials.

→ α + β = -b/a

→ 2 + 5 = –(-7)/1

→ 7 = 7/1

→ 7 = 7

→ αβ = c/a

→ 2 × 5 = 10/1

→ 10 = 10

Hence, PROVED !!