if the zeros of poynomail f(x)=2x3-15x2+37x-30 are in a.p. find them

Asked by katyalaanchal | 26th May, 2011, 12:00: AM

Expert Answer:

The given polynomial is 2x3 - 15x2 + 37x - 30.
Since the roots of the polynomial are in AP, so let the roots be a - d, a, a + d.
 
Now, using the relation between zeroes and the coefficients of the given cubic polynomial, we have:
Sum of roots = a - d + a + a + d = - (-15)/ 2 = 15/ 2
So, 3a = 15/ 2
a = 5/ 2 = 2.5
 
Now, product of roots = (a - d) (a) (a + d) = -(-30)/ 2 = 15
2.5(a2 - d2) = 15
(2.5)2 - d2 = 6
d2 = 0.25
d = 0.5
 
Thus, the zeroes of the given polynomial are 2, 2.5, and 3.

Answered by  | 27th May, 2011, 10:50: AM

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