Question

Find $b$ if the roots of the equation $24x^2+bx+25.=0$ are positive and $x_2=1.5x_1.$

Answer 1

given equation is $24x^2+bx+25$

given that $x_2=1.5x_1$

sum of roots is $\frac{-b}{24}$

so $x_1+x_2=\frac{-b}{24}$

$x_1+1.5x_1=\frac{-b}{24}$

$2.5x_1=\frac{-b}{24}$.............$\text{a}$

product of the root=$\frac{25}{24}$

$1.5x_1^2=\frac{25}{24}$

$x_1^2=\frac{25}{36}$

$x_1=\frac{5}{6}$

now, put the value of $x_1$ on equation $\text{a}$

$2.5\times \frac{5}{6}=\frac{-b}{24}$

$b=-2.5\times \frac{5}{6}\times 24$

$b=-50$ answer.