Question

4x3-24x2+23x+18=0, give that root in the form of a.p

Answer 1

root in a.p

let first root = a-d

second root = a

third root = a+d

sum of root

a-d+a+a+d = -b/a

$a - d + a + a + d = - \frac{ - 24}{4} \\ 3a = 6 \\ a = 2$

product of root

$(a - d)(a)(a + d) = \frac{ - 18}{4} \\ (2 - d)(2)(2 + d) = \frac{ - 9}{2} \\( 2)(4 - {d}^{2} ) = \frac{ - 9}{2} \\ 8 - 2 {d}^{2} = \frac{ - 9}{2} \\ 16 - 4 {d}^{2} = - 9 \\ {d}^{2} = \frac{25}{4} \\ d = \frac{5}{2}$

first root = 2- 5/2

2-2.5

first root = 0.5

second root = 2

third root = 2+2.5

4.5 answer