Question

find the zeros of polynomial and verify the relationship between its coefficient 5x^2+37x-24

Answer 1

Heya mate, Here is your answer

$\huge\red{ \mathfrak{answer}}$


$5 {x}^{2} + 37x - 24$

$5 \times 24 = 120 = 40 - 3$


$5 {x}^{2} + (40 - 3)x - 24$


$0 = 5 {x}^{2} + 40 x - 3x - 24$


$0 = 5x(x + 8) - 3(x + 8)$


$0 = (5x - 3)(x + 8)$


$i)5x - 3 = 0$



$5x = 0 + 3$


$x = \frac{3}{5}$


$so \: \alpha = \frac{3}{5}$


$ii)x + 8 = 0$


$x = 0 - 8$


$x = - 8$


$so \beta = - 8$


5x^2+37x-24

a = 5

b=37

c= -24

$\alpha + \beta = \frac{ - b}{a}$


$\frac{3}{5} + ( - 8) = \frac{ - 37}{5}$


$\frac{3}{5} - 8 = \frac{ - 37}{5}$


$\frac{3 - 40}{5} = \frac{ - 37}{5}$


$\frac{ - 37}{5} = \frac{ - 37}{5}$


$\alpha \times \beta = \frac{c}{a}$


$\frac{3}{5} \times - 8 = \frac{ - 24}{5}$


$\frac{ - 24}{5} = \frac{ - 24}{5}$


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