Question

If the zeros of the polynomial f(x)=2xcube-15xsquare+37x-30are in A.P find them

Answer 1

Hey!!!

Good Afternoon

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We have

=> f(x) = 2x³ - 15x² + 37x - 30

Since the zeros are in AP
let the zeros be (a - d)(a)(a + d)

Thus sum of zeros = -b/a

=> a - d + a + a + d = 15/2

=> 3a = 15/2

=> a = 5/2

We also know

=> Product of zeros = -d/a

=> a(a - d)(a + d) = 30/2

=> a(a² - d²) = 15

$= > \frac{5}{2} ( \frac{25}{4} - {d}^{2} ) = 15$

$= > \frac{125}{8} - \frac{5 {d}^{2} }{2} = 15$

$= > \frac{125 - 20 {d}^{2} }{8} = 15$

=> 125 - 20d² = 120

=> 20d² = 5

=> d² = 1/4

=> d = 1/2

Zeros => (a - d)(a)(a + d)

=> Zeros => (5/2 - 1/2)(5/2)(5/2 + 1/2)

=> Zeros => (2)(5/2) and 3

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Hope this helps ✌️

Have a Super Saturday Ahead