find zeros and verify them x square - 8 x + 15
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EXPLANATION.
Equation :
⇒ x² - 8x + 15 = 0.
As we know that,
Factorizes the equation into middle term splits, we get.
⇒ x² - 5x - 3x + 15 = 0.
⇒ x(x - 5) - 3(x - 5) = 0.
⇒ (x - 3)(x - 5) = 0.
⇒ x = 3 and x = 5.
Sum = 3 + 5 = 8.
Products = 3 x 5 = 15.
Quadratic equation :
⇒ x² - 8x + 15 = 0.
As we know that,
Sum of the zeroes of the quadratic polynomial.
⇒ α + β = - b/a.
⇒ α + β = -(-8)/1 = 8.
Products of the zeroes of the quadratic polynomial.
⇒ αβ = c/a.
⇒ αβ = (15)/(1) = 15.
As we know that,
Formula of the quadratic polynomial.
⇒ x² - (α + β)x + αβ.
Put the values in the equation, we get.
⇒ x² - (8)x + 15 = 0.
⇒ x² - 8x + 15 = 0.
Hence Proved.
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