Question

If the zeros of the polynomial F(x)=2x³-15x²+37x-30 are in A.p.find them​

Answer 1

Answer:

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Step-by-step explanation:

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.