Question

20
solve 4x3 - 24x² +23x +18=0; given
that the roots of this
this eqreation are
in arithmetic progression
ASTORM​

Answer 1

Step-by-step explanation:

Let a – d, a, a + d are the roots of the given equation.

Now, sum of the roots a – d + a + a + d = 24/4

3a = 6 a = 2

Product of the roots (a – d)a(a + d)

= −18/4 a(a2 – d2)

= – 9/2 = 2(4 – d2)

= – 9/2 4(4 – d2)

= – 9 16 – 4d2

= – 9 4d2

= 25 d

= ±5/2

∴ roots are -1/2, 2 and 9/2

Answer 2

Answer:

-1/2, 2 and 9/2

Step-by-step explanation:

Let a – d, a, a + d are the roots of the given equation.

If the equation is of the form ax³+bx²+cx+d = 0, then Sum of the roots is given by -b/a

Now, sum of the roots a – d + a + a + d = -b/a = -(-24/4) = 24/4 = 6

=> 3a = 6

$=>\boxed {\text{a = 2}}$

Now, Product of the roots (a – d)a(a + d)

=> −18/4 = a(a² – d²)

=> – 9/2 = 2(4 – d²)

=> – 9/2 = 2(4 – d²)

=> – 9/4 = 4 - d²

=> d² = 4 + (9/4)

=> d² = (16+9)/4

=> d² = 25/4

=> d = ±5/2

∴ roots are -1/2, 2 and 9/2

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