Question

If a – b,a & a + b are zeroes of the polynomial f(x) = 2x³ – 6x² + 5x – 7, then the value of a is (Give explanation)

a) 0
b) 1
c)2
d) 3​

Answer 1

Answer:

If a – b,a & a + b are zeroes of the polynomial f(x) = 2x³ – 6x² + 5x – 7, then

$a - b + a + a + b = - \frac{ - 6}{2} = 3 \\ \implies \: 3a = 3 \\ \implies \: a = \frac{3}{3} \\ \therefore \: a = 1$

so option b) 1 is the correct answer

Note :

$If \: \alpha \: , \: \beta \: \gamma \: \: are \: zeroes \: of \\ \: the \: \: polynomial \: \: \: \\ p(x) = a {x}^{3} + b {x}^{2} + cx + d \: \: \: \: the n\\ \\ \alpha + \beta + \gamma = - \frac{b}{a}$