If a – b, a and a + b are zeros of the polynomial f (x) = 2x³ – 6x² + 5x – 7, write the value of a.

AshjexBG AshjexBG Best Answer 1 year ago

a = 1 Step-by-step explanation:Given----> ( a - b ) , a and ( a + b ) are zeroes of f ( x ) = 2x³ - 6x² + 5x - 7 To find ----> Value of a SOLUTION-----> We know that , If a cubic POLYNOMIAL p ( x ) = ax³ + bx² + cx + d , and its zeroes are α , β , γ , then , α + β + γ = - Coefficient of x² / Coefficient of x³Now , ATQ, ( a - b ) , a , ( a + b ) are zeroes of f ( x ) = 2x³ - 6x² + 5x - 7 Now , we know that , Sum of zeroes = -Coefficient of x²/Coefficient ofx³ ( a - b ) + a + ( a + b ) = - ( -6 ) / 2 => 3a = 3 => a = 3 / 3 => a = 1 Additional information------> 1) If , p ( x ) = ax³ + bx² + cx + d , and its zeroes are α , β and γ . α + β + γ = - Coefficient of x² / Coefficient of x³αβ + βγ + yα = Coefficient of x / Coeficient of x³α β γ = - Constat term / Coefficient of x³

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