Verify the relationship between the zeroes and coefficients of the following polynomail x^2+11×+18
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We have,
x² + 11x + 18
★ By Splitting middle term
⇒ x² + 9x + 2x + 18
⇒ x ( x + 9 ) + 2 ( x + 9 )
⇒ ( x + 9 ) ( x + 2 )
So, to find zeroes of polynomial : x² + 11x + 18 will be 0,
Hence ( x + 9 ) = 0 and ( x + 2 ) = 0
⇒ x = -9 and x = -2
Therefore, the zeroes of the polynomial are -9 and -2 .
Verification:-
★Sum of the zeroes = - Coefficient of x/Coefficient of x²
⇒ ( -9 ) + ( -2 ) = - 11 / 1
⇒ - 11 = -11
L.H.S = R.H.S
★ Product of the zeroes = Constant term/Coefficient of x²
⇒ ( -9 ) × ( -2 ) = 18 / 1
⇒ 18 = 18
L.H.S = R.H.S
Verified.
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