Q14 of 90 Page 2

Find a cubic polynomial with the sum of its zeroes are 0, – 7 and – 6 respectively.

Let the zeroes be α, β and γ.


Then, we have


α + β + γ = 0


αβ + βγ + γα = – 7


and αβγ = – 6


Now, required cubic polynomial


= x3 – (α + β + γ) x2 + (αβ + βγ + γα)x – αβγ


= x3 – (0) x2 + ( – 7)x – ( – 6)


= x3 – 7x + 6


So, x3 – 7x + 6 is the required cubic polynomial.


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